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G = C24.18D14  order 448 = 26·7

18th non-split extension by C24 of D14 acting via D14/C7=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.18D14, (D4×C14)⋊14C4, (C2×D4)⋊6Dic7, (C2×Dic7)⋊18D4, C14.101(C4×D4), C2.18(D4×Dic7), (C22×D4).6D7, C23⋊2(C2×Dic7), C14.67C22≀C2, (C23×Dic7)⋊2C2, C22.120(D4×D7), C2.5(C23⋊D14), (C22×C14).109D4, (C22×C4).151D14, C23.43(C7⋊D4), C7⋊5(C23.23D4), C14.128(C4⋊D4), C22⋊1(C23.D7), C14.C42⋊44C2, C2.7(Dic7⋊D4), (C23×C14).46C22, C23.305(C22×D7), C22.61(D4⋊2D7), (C22×C14).365C23, (C22×C28).394C22, C22.51(C22×Dic7), C14.83(C22.D4), C2.5(C23.18D14), (C22×Dic7).196C22, (C2×C28)⋊22(C2×C4), (D4×C2×C14).11C2, (C2×C4)⋊3(C2×Dic7), (C22×C14)⋊7(C2×C4), (C2×C23.D7)⋊9C2, (C2×C14)⋊3(C22⋊C4), (C2×C14).377(C2×D4), C14.75(C2×C22⋊C4), C22.91(C2×C7⋊D4), C2.11(C2×C23.D7), (C2×C14).161(C4○D4), (C2×C14).196(C22×C4), SmallGroup(448,754)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C24.18D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C23×Dic7 — C24.18D14
Lower central
C7 — C2×C14 — C24.18D14
Upper central
C1 — C23 — C22×D4

Generators and relations for C24.18D14
 G = < a,b,c,d,e,f | a2=b2=c2=d2=e14=1, f2=b, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e-1 >

Subgroups: 1044 in 286 conjugacy classes, 91 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, C14, C14, C14, C22⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, Dic7, C28, C2×C14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C23×C4, C22×D4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C22×C14, C23.23D4, C23.D7, C22×Dic7, C22×Dic7, C22×C28, D4×C14, D4×C14, C23×C14, C14.C42, C2×C23.D7, C2×C23.D7, C23×Dic7, D4×C2×C14, C24.18D14
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, Dic7, D14, C2×C22⋊C4, C4×D4, C22≀C2, C4⋊D4, C22.D4, C2×Dic7, C7⋊D4, C22×D7, C23.23D4, C23.D7, D4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, D4×Dic7, C23.18D14, C23⋊D14, Dic7⋊D4, C2×C23.D7, C24.18D14

Smallest permutation representation of C24.18D14
►On 224 points
Generators in S224
(1 152)(2 96)(3 154)(4 98)(5 142)(6 86)(7 144)(8 88)(9 146)(10 90)(11 148)(12 92)(13 150)(14 94)(15 64)(16 106)(17 66)(18 108)(19 68)(20 110)(21 70)(22 112)(23 58)(24 100)(25 60)(26 102)(27 62)(28 104)(29 54)(30 126)(31 56)(32 114)(33 44)(34 116)(35 46)(36 118)(37 48)(38 120)(39 50)(40 122)(41 52)(42 124)(43 129)(45 131)(47 133)(49 135)(51 137)(53 139)(55 127)(57 75)(59 77)(61 79)(63 81)(65 83)(67 71)(69 73)(72 109)(74 111)(76 99)(78 101)(80 103)(82 105)(84 107)(85 219)(87 221)(89 223)(91 211)(93 213)(95 215)(97 217)(113 128)(115 130)(117 132)(119 134)(121 136)(123 138)(125 140)(141 218)(143 220)(145 222)(147 224)(149 212)(151 214)(153 216)(155 187)(156 172)(157 189)(158 174)(159 191)(160 176)(161 193)(162 178)(163 195)(164 180)(165 183)(166 182)(167 185)(168 170)(169 203)(171 205)(173 207)(175 209)(177 197)(179 199)(181 201)(184 202)(186 204)(188 206)(190 208)(192 210)(194 198)(196 200)

(1 163)(2 164)(3 165)(4 166)(5 167)(6 168)(7 155)(8 156)(9 157)(10 158)(11 159)(12 160)(13 161)(14 162)(15 113)(16 114)(17 115)(18 116)(19 117)(20 118)(21 119)(22 120)(23 121)(24 122)(25 123)(26 124)(27 125)(28 126)(29 103)(30 104)(31 105)(32 106)(33 107)(34 108)(35 109)(36 110)(37 111)(38 112)(39 99)(40 100)(41 101)(42 102)(43 83)(44 84)(45 71)(46 72)(47 73)(48 74)(49 75)(50 76)(51 77)(52 78)(53 79)(54 80)(55 81)(56 82)(57 135)(58 136)(59 137)(60 138)(61 139)(62 140)(63 127)(64 128)(65 129)(66 130)(67 131)(68 132)(69 133)(70 134)(85 169)(86 170)(87 171)(88 172)(89 173)(90 174)(91 175)(92 176)(93 177)(94 178)(95 179)(96 180)(97 181)(98 182)(141 184)(142 185)(143 186)(144 187)(145 188)(146 189)(147 190)(148 191)(149 192)(150 193)(151 194)(152 195)(153 196)(154 183)(197 213)(198 214)(199 215)(200 216)(201 217)(202 218)(203 219)(204 220)(205 221)(206 222)(207 223)(208 224)(209 211)(210 212)

(1 156)(2 157)(3 158)(4 159)(5 160)(6 161)(7 162)(8 163)(9 164)(10 165)(11 166)(12 167)(13 168)(14 155)(15 49)(16 50)(17 51)(18 52)(19 53)(20 54)(21 55)(22 56)(23 43)(24 44)(25 45)(26 46)(27 47)(28 48)(29 110)(30 111)(31 112)(32 99)(33 100)(34 101)(35 102)(36 103)(37 104)(38 105)(39 106)(40 107)(41 108)(42 109)(57 128)(58 129)(59 130)(60 131)(61 132)(62 133)(63 134)(64 135)(65 136)(66 137)(67 138)(68 139)(69 140)(70 127)(71 123)(72 124)(73 125)(74 126)(75 113)(76 114)(77 115)(78 116)(79 117)(80 118)(81 119)(82 120)(83 121)(84 122)(85 192)(86 193)(87 194)(88 195)(89 196)(90 183)(91 184)(92 185)(93 186)(94 187)(95 188)(96 189)(97 190)(98 191)(141 175)(142 176)(143 177)(144 178)(145 179)(146 180)(147 181)(148 182)(149 169)(150 170)(151 171)(152 172)(153 173)(154 174)(197 220)(198 221)(199 222)(200 223)(201 224)(202 211)(203 212)(204 213)(205 214)(206 215)(207 216)(208 217)(209 218)(210 219)

(1 215)(2 216)(3 217)(4 218)(5 219)(6 220)(7 221)(8 222)(9 223)(10 224)(11 211)(12 212)(13 213)(14 214)(15 82)(16 83)(17 84)(18 71)(19 72)(20 73)(21 74)(22 75)(23 76)(24 77)(25 78)(26 79)(27 80)(28 81)(29 140)(30 127)(31 128)(32 129)(33 130)(34 131)(35 132)(36 133)(37 134)(38 135)(39 136)(40 137)(41 138)(42 139)(43 114)(44 115)(45 116)(46 117)(47 118)(48 119)(49 120)(50 121)(51 122)(52 123)(53 124)(54 125)(55 126)(56 113)(57 112)(58 99)(59 100)(60 101)(61 102)(62 103)(63 104)(64 105)(65 106)(66 107)(67 108)(68 109)(69 110)(70 111)(85 142)(86 143)(87 144)(88 145)(89 146)(90 147)(91 148)(92 149)(93 150)(94 151)(95 152)(96 153)(97 154)(98 141)(155 205)(156 206)(157 207)(158 208)(159 209)(160 210)(161 197)(162 198)(163 199)(164 200)(165 201)(166 202)(167 203)(168 204)(169 185)(170 186)(171 187)(172 188)(173 189)(174 190)(175 191)(176 192)(177 193)(178 194)(179 195)(180 196)(181 183)(182 184)

(1 2 3 4 5 6 7 8 9 10 11 12 13 14)(15 16 17 18 19 20 21 22 23 24 25 26 27 28)(29 30 31 32 33 34 35 36 37 38 39 40 41 42)(43 44 45 46 47 48 49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64 65 66 67 68 69 70)(71 72 73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96 97 98)(99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126)(127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154)(155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182)(183 184 185 186 187 188 189 190 191 192 193 194 195 196)(197 198 199 200 201 202 203 204 205 206 207 208 209 210)(211 212 213 214 215 216 217 218 219 220 221 222 223 224)

(1 37 163 111)(2 36 164 110)(3 35 165 109)(4 34 166 108)(5 33 167 107)(6 32 168 106)(7 31 155 105)(8 30 156 104)(9 29 157 103)(10 42 158 102)(11 41 159 101)(12 40 160 100)(13 39 161 99)(14 38 162 112)(15 178 113 94)(16 177 114 93)(17 176 115 92)(18 175 116 91)(19 174 117 90)(20 173 118 89)(21 172 119 88)(22 171 120 87)(23 170 121 86)(24 169 122 85)(25 182 123 98)(26 181 124 97)(27 180 125 96)(28 179 126 95)(43 150 83 193)(44 149 84 192)(45 148 71 191)(46 147 72 190)(47 146 73 189)(48 145 74 188)(49 144 75 187)(50 143 76 186)(51 142 77 185)(52 141 78 184)(53 154 79 183)(54 153 80 196)(55 152 81 195)(56 151 82 194)(57 214 135 198)(58 213 136 197)(59 212 137 210)(60 211 138 209)(61 224 139 208)(62 223 140 207)(63 222 127 206)(64 221 128 205)(65 220 129 204)(66 219 130 203)(67 218 131 202)(68 217 132 201)(69 216 133 200)(70 215 134 199)
 
G:=sub<Sym(224)| (1,152)(2,96)(3,154)(4,98)(5,142)(6,86)(7,144)(8,88)(9,146)(10,90)(11,148)(12,92)(13,150)(14,94)(15,64)(16,106)(17,66)(18,108)(19,68)(20,110)(21,70)(22,112)(23,58)(24,100)(25,60)(26,102)(27,62)(28,104)(29,54)(30,126)(31,56)(32,114)(33,44)(34,116)(35,46)(36,118)(37,48)(38,120)(39,50)(40,122)(41,52)(42,124)(43,129)(45,131)(47,133)(49,135)(51,137)(53,139)(55,127)(57,75)(59,77)(61,79)(63,81)(65,83)(67,71)(69,73)(72,109)(74,111)(76,99)(78,101)(80,103)(82,105)(84,107)(85,219)(87,221)(89,223)(91,211)(93,213)(95,215)(97,217)(113,128)(115,130)(117,132)(119,134)(121,136)(123,138)(125,140)(141,218)(143,220)(145,222)(147,224)(149,212)(151,214)(153,216)(155,187)(156,172)(157,189)(158,174)(159,191)(160,176)(161,193)(162,178)(163,195)(164,180)(165,183)(166,182)(167,185)(168,170)(169,203)(171,205)(173,207)(175,209)(177,197)(179,199)(181,201)(184,202)(186,204)(188,206)(190,208)(192,210)(194,198)(196,200), (1,163)(2,164)(3,165)(4,166)(5,167)(6,168)(7,155)(8,156)(9,157)(10,158)(11,159)(12,160)(13,161)(14,162)(15,113)(16,114)(17,115)(18,116)(19,117)(20,118)(21,119)(22,120)(23,121)(24,122)(25,123)(26,124)(27,125)(28,126)(29,103)(30,104)(31,105)(32,106)(33,107)(34,108)(35,109)(36,110)(37,111)(38,112)(39,99)(40,100)(41,101)(42,102)(43,83)(44,84)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(53,79)(54,80)(55,81)(56,82)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,127)(64,128)(65,129)(66,130)(67,131)(68,132)(69,133)(70,134)(85,169)(86,170)(87,171)(88,172)(89,173)(90,174)(91,175)(92,176)(93,177)(94,178)(95,179)(96,180)(97,181)(98,182)(141,184)(142,185)(143,186)(144,187)(145,188)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,196)(154,183)(197,213)(198,214)(199,215)(200,216)(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)(208,224)(209,211)(210,212), (1,156)(2,157)(3,158)(4,159)(5,160)(6,161)(7,162)(8,163)(9,164)(10,165)(11,166)(12,167)(13,168)(14,155)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,110)(30,111)(31,112)(32,99)(33,100)(34,101)(35,102)(36,103)(37,104)(38,105)(39,106)(40,107)(41,108)(42,109)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,127)(71,123)(72,124)(73,125)(74,126)(75,113)(76,114)(77,115)(78,116)(79,117)(80,118)(81,119)(82,120)(83,121)(84,122)(85,192)(86,193)(87,194)(88,195)(89,196)(90,183)(91,184)(92,185)(93,186)(94,187)(95,188)(96,189)(97,190)(98,191)(141,175)(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)(149,169)(150,170)(151,171)(152,172)(153,173)(154,174)(197,220)(198,221)(199,222)(200,223)(201,224)(202,211)(203,212)(204,213)(205,214)(206,215)(207,216)(208,217)(209,218)(210,219), (1,215)(2,216)(3,217)(4,218)(5,219)(6,220)(7,221)(8,222)(9,223)(10,224)(11,211)(12,212)(13,213)(14,214)(15,82)(16,83)(17,84)(18,71)(19,72)(20,73)(21,74)(22,75)(23,76)(24,77)(25,78)(26,79)(27,80)(28,81)(29,140)(30,127)(31,128)(32,129)(33,130)(34,131)(35,132)(36,133)(37,134)(38,135)(39,136)(40,137)(41,138)(42,139)(43,114)(44,115)(45,116)(46,117)(47,118)(48,119)(49,120)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,113)(57,112)(58,99)(59,100)(60,101)(61,102)(62,103)(63,104)(64,105)(65,106)(66,107)(67,108)(68,109)(69,110)(70,111)(85,142)(86,143)(87,144)(88,145)(89,146)(90,147)(91,148)(92,149)(93,150)(94,151)(95,152)(96,153)(97,154)(98,141)(155,205)(156,206)(157,207)(158,208)(159,209)(160,210)(161,197)(162,198)(163,199)(164,200)(165,201)(166,202)(167,203)(168,204)(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)(177,193)(178,194)(179,195)(180,196)(181,183)(182,184), (1,2,3,4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70)(71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98)(99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126)(127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154)(155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,37,163,111)(2,36,164,110)(3,35,165,109)(4,34,166,108)(5,33,167,107)(6,32,168,106)(7,31,155,105)(8,30,156,104)(9,29,157,103)(10,42,158,102)(11,41,159,101)(12,40,160,100)(13,39,161,99)(14,38,162,112)(15,178,113,94)(16,177,114,93)(17,176,115,92)(18,175,116,91)(19,174,117,90)(20,173,118,89)(21,172,119,88)(22,171,120,87)(23,170,121,86)(24,169,122,85)(25,182,123,98)(26,181,124,97)(27,180,125,96)(28,179,126,95)(43,150,83,193)(44,149,84,192)(45,148,71,191)(46,147,72,190)(47,146,73,189)(48,145,74,188)(49,144,75,187)(50,143,76,186)(51,142,77,185)(52,141,78,184)(53,154,79,183)(54,153,80,196)(55,152,81,195)(56,151,82,194)(57,214,135,198)(58,213,136,197)(59,212,137,210)(60,211,138,209)(61,224,139,208)(62,223,140,207)(63,222,127,206)(64,221,128,205)(65,220,129,204)(66,219,130,203)(67,218,131,202)(68,217,132,201)(69,216,133,200)(70,215,134,199)>;
 
G:=Group( (1,152)(2,96)(3,154)(4,98)(5,142)(6,86)(7,144)(8,88)(9,146)(10,90)(11,148)(12,92)(13,150)(14,94)(15,64)(16,106)(17,66)(18,108)(19,68)(20,110)(21,70)(22,112)(23,58)(24,100)(25,60)(26,102)(27,62)(28,104)(29,54)(30,126)(31,56)(32,114)(33,44)(34,116)(35,46)(36,118)(37,48)(38,120)(39,50)(40,122)(41,52)(42,124)(43,129)(45,131)(47,133)(49,135)(51,137)(53,139)(55,127)(57,75)(59,77)(61,79)(63,81)(65,83)(67,71)(69,73)(72,109)(74,111)(76,99)(78,101)(80,103)(82,105)(84,107)(85,219)(87,221)(89,223)(91,211)(93,213)(95,215)(97,217)(113,128)(115,130)(117,132)(119,134)(121,136)(123,138)(125,140)(141,218)(143,220)(145,222)(147,224)(149,212)(151,214)(153,216)(155,187)(156,172)(157,189)(158,174)(159,191)(160,176)(161,193)(162,178)(163,195)(164,180)(165,183)(166,182)(167,185)(168,170)(169,203)(171,205)(173,207)(175,209)(177,197)(179,199)(181,201)(184,202)(186,204)(188,206)(190,208)(192,210)(194,198)(196,200), (1,163)(2,164)(3,165)(4,166)(5,167)(6,168)(7,155)(8,156)(9,157)(10,158)(11,159)(12,160)(13,161)(14,162)(15,113)(16,114)(17,115)(18,116)(19,117)(20,118)(21,119)(22,120)(23,121)(24,122)(25,123)(26,124)(27,125)(28,126)(29,103)(30,104)(31,105)(32,106)(33,107)(34,108)(35,109)(36,110)(37,111)(38,112)(39,99)(40,100)(41,101)(42,102)(43,83)(44,84)(45,71)(46,72)(47,73)(48,74)(49,75)(50,76)(51,77)(52,78)(53,79)(54,80)(55,81)(56,82)(57,135)(58,136)(59,137)(60,138)(61,139)(62,140)(63,127)(64,128)(65,129)(66,130)(67,131)(68,132)(69,133)(70,134)(85,169)(86,170)(87,171)(88,172)(89,173)(90,174)(91,175)(92,176)(93,177)(94,178)(95,179)(96,180)(97,181)(98,182)(141,184)(142,185)(143,186)(144,187)(145,188)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,196)(154,183)(197,213)(198,214)(199,215)(200,216)(201,217)(202,218)(203,219)(204,220)(205,221)(206,222)(207,223)(208,224)(209,211)(210,212), (1,156)(2,157)(3,158)(4,159)(5,160)(6,161)(7,162)(8,163)(9,164)(10,165)(11,166)(12,167)(13,168)(14,155)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,110)(30,111)(31,112)(32,99)(33,100)(34,101)(35,102)(36,103)(37,104)(38,105)(39,106)(40,107)(41,108)(42,109)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,127)(71,123)(72,124)(73,125)(74,126)(75,113)(76,114)(77,115)(78,116)(79,117)(80,118)(81,119)(82,120)(83,121)(84,122)(85,192)(86,193)(87,194)(88,195)(89,196)(90,183)(91,184)(92,185)(93,186)(94,187)(95,188)(96,189)(97,190)(98,191)(141,175)(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)(149,169)(150,170)(151,171)(152,172)(153,173)(154,174)(197,220)(198,221)(199,222)(200,223)(201,224)(202,211)(203,212)(204,213)(205,214)(206,215)(207,216)(208,217)(209,218)(210,219), (1,215)(2,216)(3,217)(4,218)(5,219)(6,220)(7,221)(8,222)(9,223)(10,224)(11,211)(12,212)(13,213)(14,214)(15,82)(16,83)(17,84)(18,71)(19,72)(20,73)(21,74)(22,75)(23,76)(24,77)(25,78)(26,79)(27,80)(28,81)(29,140)(30,127)(31,128)(32,129)(33,130)(34,131)(35,132)(36,133)(37,134)(38,135)(39,136)(40,137)(41,138)(42,139)(43,114)(44,115)(45,116)(46,117)(47,118)(48,119)(49,120)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,113)(57,112)(58,99)(59,100)(60,101)(61,102)(62,103)(63,104)(64,105)(65,106)(66,107)(67,108)(68,109)(69,110)(70,111)(85,142)(86,143)(87,144)(88,145)(89,146)(90,147)(91,148)(92,149)(93,150)(94,151)(95,152)(96,153)(97,154)(98,141)(155,205)(156,206)(157,207)(158,208)(159,209)(160,210)(161,197)(162,198)(163,199)(164,200)(165,201)(166,202)(167,203)(168,204)(169,185)(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)(177,193)(178,194)(179,195)(180,196)(181,183)(182,184), (1,2,3,4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70)(71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98)(99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126)(127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154)(155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,37,163,111)(2,36,164,110)(3,35,165,109)(4,34,166,108)(5,33,167,107)(6,32,168,106)(7,31,155,105)(8,30,156,104)(9,29,157,103)(10,42,158,102)(11,41,159,101)(12,40,160,100)(13,39,161,99)(14,38,162,112)(15,178,113,94)(16,177,114,93)(17,176,115,92)(18,175,116,91)(19,174,117,90)(20,173,118,89)(21,172,119,88)(22,171,120,87)(23,170,121,86)(24,169,122,85)(25,182,123,98)(26,181,124,97)(27,180,125,96)(28,179,126,95)(43,150,83,193)(44,149,84,192)(45,148,71,191)(46,147,72,190)(47,146,73,189)(48,145,74,188)(49,144,75,187)(50,143,76,186)(51,142,77,185)(52,141,78,184)(53,154,79,183)(54,153,80,196)(55,152,81,195)(56,151,82,194)(57,214,135,198)(58,213,136,197)(59,212,137,210)(60,211,138,209)(61,224,139,208)(62,223,140,207)(63,222,127,206)(64,221,128,205)(65,220,129,204)(66,219,130,203)(67,218,131,202)(68,217,132,201)(69,216,133,200)(70,215,134,199) );
 
G=PermutationGroup([[(1,152),(2,96),(3,154),(4,98),(5,142),(6,86),(7,144),(8,88),(9,146),(10,90),(11,148),(12,92),(13,150),(14,94),(15,64),(16,106),(17,66),(18,108),(19,68),(20,110),(21,70),(22,112),(23,58),(24,100),(25,60),(26,102),(27,62),(28,104),(29,54),(30,126),(31,56),(32,114),(33,44),(34,116),(35,46),(36,118),(37,48),(38,120),(39,50),(40,122),(41,52),(42,124),(43,129),(45,131),(47,133),(49,135),(51,137),(53,139),(55,127),(57,75),(59,77),(61,79),(63,81),(65,83),(67,71),(69,73),(72,109),(74,111),(76,99),(78,101),(80,103),(82,105),(84,107),(85,219),(87,221),(89,223),(91,211),(93,213),(95,215),(97,217),(113,128),(115,130),(117,132),(119,134),(121,136),(123,138),(125,140),(141,218),(143,220),(145,222),(147,224),(149,212),(151,214),(153,216),(155,187),(156,172),(157,189),(158,174),(159,191),(160,176),(161,193),(162,178),(163,195),(164,180),(165,183),(166,182),(167,185),(168,170),(169,203),(171,205),(173,207),(175,209),(177,197),(179,199),(181,201),(184,202),(186,204),(188,206),(190,208),(192,210),(194,198),(196,200)], [(1,163),(2,164),(3,165),(4,166),(5,167),(6,168),(7,155),(8,156),(9,157),(10,158),(11,159),(12,160),(13,161),(14,162),(15,113),(16,114),(17,115),(18,116),(19,117),(20,118),(21,119),(22,120),(23,121),(24,122),(25,123),(26,124),(27,125),(28,126),(29,103),(30,104),(31,105),(32,106),(33,107),(34,108),(35,109),(36,110),(37,111),(38,112),(39,99),(40,100),(41,101),(42,102),(43,83),(44,84),(45,71),(46,72),(47,73),(48,74),(49,75),(50,76),(51,77),(52,78),(53,79),(54,80),(55,81),(56,82),(57,135),(58,136),(59,137),(60,138),(61,139),(62,140),(63,127),(64,128),(65,129),(66,130),(67,131),(68,132),(69,133),(70,134),(85,169),(86,170),(87,171),(88,172),(89,173),(90,174),(91,175),(92,176),(93,177),(94,178),(95,179),(96,180),(97,181),(98,182),(141,184),(142,185),(143,186),(144,187),(145,188),(146,189),(147,190),(148,191),(149,192),(150,193),(151,194),(152,195),(153,196),(154,183),(197,213),(198,214),(199,215),(200,216),(201,217),(202,218),(203,219),(204,220),(205,221),(206,222),(207,223),(208,224),(209,211),(210,212)], [(1,156),(2,157),(3,158),(4,159),(5,160),(6,161),(7,162),(8,163),(9,164),(10,165),(11,166),(12,167),(13,168),(14,155),(15,49),(16,50),(17,51),(18,52),(19,53),(20,54),(21,55),(22,56),(23,43),(24,44),(25,45),(26,46),(27,47),(28,48),(29,110),(30,111),(31,112),(32,99),(33,100),(34,101),(35,102),(36,103),(37,104),(38,105),(39,106),(40,107),(41,108),(42,109),(57,128),(58,129),(59,130),(60,131),(61,132),(62,133),(63,134),(64,135),(65,136),(66,137),(67,138),(68,139),(69,140),(70,127),(71,123),(72,124),(73,125),(74,126),(75,113),(76,114),(77,115),(78,116),(79,117),(80,118),(81,119),(82,120),(83,121),(84,122),(85,192),(86,193),(87,194),(88,195),(89,196),(90,183),(91,184),(92,185),(93,186),(94,187),(95,188),(96,189),(97,190),(98,191),(141,175),(142,176),(143,177),(144,178),(145,179),(146,180),(147,181),(148,182),(149,169),(150,170),(151,171),(152,172),(153,173),(154,174),(197,220),(198,221),(199,222),(200,223),(201,224),(202,211),(203,212),(204,213),(205,214),(206,215),(207,216),(208,217),(209,218),(210,219)], [(1,215),(2,216),(3,217),(4,218),(5,219),(6,220),(7,221),(8,222),(9,223),(10,224),(11,211),(12,212),(13,213),(14,214),(15,82),(16,83),(17,84),(18,71),(19,72),(20,73),(21,74),(22,75),(23,76),(24,77),(25,78),(26,79),(27,80),(28,81),(29,140),(30,127),(31,128),(32,129),(33,130),(34,131),(35,132),(36,133),(37,134),(38,135),(39,136),(40,137),(41,138),(42,139),(43,114),(44,115),(45,116),(46,117),(47,118),(48,119),(49,120),(50,121),(51,122),(52,123),(53,124),(54,125),(55,126),(56,113),(57,112),(58,99),(59,100),(60,101),(61,102),(62,103),(63,104),(64,105),(65,106),(66,107),(67,108),(68,109),(69,110),(70,111),(85,142),(86,143),(87,144),(88,145),(89,146),(90,147),(91,148),(92,149),(93,150),(94,151),(95,152),(96,153),(97,154),(98,141),(155,205),(156,206),(157,207),(158,208),(159,209),(160,210),(161,197),(162,198),(163,199),(164,200),(165,201),(166,202),(167,203),(168,204),(169,185),(170,186),(171,187),(172,188),(173,189),(174,190),(175,191),(176,192),(177,193),(178,194),(179,195),(180,196),(181,183),(182,184)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14),(15,16,17,18,19,20,21,22,23,24,25,26,27,28),(29,30,31,32,33,34,35,36,37,38,39,40,41,42),(43,44,45,46,47,48,49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64,65,66,67,68,69,70),(71,72,73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96,97,98),(99,100,101,102,103,104,105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120,121,122,123,124,125,126),(127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154),(155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182),(183,184,185,186,187,188,189,190,191,192,193,194,195,196),(197,198,199,200,201,202,203,204,205,206,207,208,209,210),(211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,37,163,111),(2,36,164,110),(3,35,165,109),(4,34,166,108),(5,33,167,107),(6,32,168,106),(7,31,155,105),(8,30,156,104),(9,29,157,103),(10,42,158,102),(11,41,159,101),(12,40,160,100),(13,39,161,99),(14,38,162,112),(15,178,113,94),(16,177,114,93),(17,176,115,92),(18,175,116,91),(19,174,117,90),(20,173,118,89),(21,172,119,88),(22,171,120,87),(23,170,121,86),(24,169,122,85),(25,182,123,98),(26,181,124,97),(27,180,125,96),(28,179,126,95),(43,150,83,193),(44,149,84,192),(45,148,71,191),(46,147,72,190),(47,146,73,189),(48,145,74,188),(49,144,75,187),(50,143,76,186),(51,142,77,185),(52,141,78,184),(53,154,79,183),(54,153,80,196),(55,152,81,195),(56,151,82,194),(57,214,135,198),(58,213,136,197),(59,212,137,210),(60,211,138,209),(61,224,139,208),(62,223,140,207),(63,222,127,206),(64,221,128,205),(65,220,129,204),(66,219,130,203),(67,218,131,202),(68,217,132,201),(69,216,133,200),(70,215,134,199)]])
 

88 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M4A4B4C···4J4K4L4M4N7A7B7C14A···14U14V···14AS28A···28L
order12···2222222444···4444477714···1414···1428···28
size11···12222444414···14282828282222···24···44···4

88 irreducible representations

dim1111112222222244
type+++++++++-++-
imageC1C2C2C2C2C4D4D4D7C4○D4D14Dic7D14C7⋊D4D4×D7D4⋊2D7
kernelC24.18D14C14.C42C2×C23.D7C23×Dic7D4×C2×C14D4×C14C2×Dic7C22×C14C22×D4C2×C14C22×C4C2×D4C24C23C22C22
# reps123118443431262466

Matrix representation of C24.18D14 ►in GL6(𝔽29)

18140000
8110000
001000
000100
00001016
00002119
,
100000
010000
0028000
0002800
0000280
0000028
,
2800000
0280000
001000
000100
000010
000001
,
100000
010000
001000
000100
0000280
0000028
,
25190000
1510000
001400
0052100
0000280
0000231
,
25190000
1640000
0071600
00152200
0000120
00001417

G:=sub<GL(6,GF(29))| [18,8,0,0,0,0,14,11,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,10,21,0,0,0,0,16,19],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[25,15,0,0,0,0,19,1,0,0,0,0,0,0,1,5,0,0,0,0,4,21,0,0,0,0,0,0,28,23,0,0,0,0,0,1],[25,16,0,0,0,0,19,4,0,0,0,0,0,0,7,15,0,0,0,0,16,22,0,0,0,0,0,0,12,14,0,0,0,0,0,17] >;
 

C24.18D14 in GAP, Magma, Sage, TeX 

C_2^4._{18}D_{14}
 
% in TeX
 
G:=Group("C2^4.18D14");
 
// GroupNames label
 
G:=SmallGroup(448,754);
 
// by ID
 
G=gap.SmallGroup(448,754);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,422,387,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^14=1,f^2=b,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*c*d,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=e^-1>;
 
// generators/relations
 

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