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G = C24.10D14  order 448 = 26·7

10th non-split extension by C24 of D14 acting via D14/C7=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C24.10D14, C23.14D28, (C2×C28).51D4, C2.6(C28⋊7D4), (C22×C4).91D14, (C22×C14).65D4, C14.58(C4⋊D4), C22.125(C2×D28), C7⋊4(C23.11D4), C14.C42⋊15C2, C2.6(C28.17D4), C14.38(C4.4D4), C22.98(C4○D28), (C22×C28).60C22, (C23×C14).36C22, C23.370(C22×D7), C14.16(C42⋊2C2), C22.96(D4⋊2D7), (C22×C14).328C23, C14.73(C22.D4), C2.14(C23.D14), C2.16(C22.D28), C2.8(C23.18D14), (C22×Dic7).42C22, (C2×C4⋊Dic7)⋊12C2, (C2×C14).432(C2×D4), (C2×C4).30(C7⋊D4), (C2×C22⋊C4).15D7, (C14×C22⋊C4).16C2, C22.126(C2×C7⋊D4), (C2×C23.D7).15C2, (C2×C14).144(C4○D4), SmallGroup(448,487)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C22×C14 — C24.10D14
Chief series
C1 — C7 — C14 — C2×C14 — C22×C14 — C22×Dic7 — C2×C4⋊Dic7 — C24.10D14
Lower central
C7 — C22×C14 — C24.10D14
Upper central
C1 — C23 — C2×C22⋊C4

Generators and relations for C24.10D14
 G = < a,b,c,d,e | a2=b2=c2=d28=1, e2=c, ab=ba, dad-1=ac=ca, eae-1=abc, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 692 in 170 conjugacy classes, 59 normal (27 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C23, C23, C23, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C24, Dic7, C28, C2×C14, C2×C14, C2×C14, C2.C42, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C2×Dic7, C2×C28, C2×C28, C22×C14, C22×C14, C22×C14, C23.11D4, C4⋊Dic7, C23.D7, C7×C22⋊C4, C22×Dic7, C22×C28, C23×C14, C14.C42, C14.C42, C2×C4⋊Dic7, C2×C23.D7, C14×C22⋊C4, C24.10D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C22.D4, C4.4D4, C42⋊2C2, D28, C7⋊D4, C22×D7, C23.11D4, C2×D28, C4○D28, D4⋊2D7, C2×C7⋊D4, C23.D14, C22.D28, C28⋊7D4, C23.18D14, C28.17D4, C24.10D14

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

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

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

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

82 conjugacy classes

class 1 2A···2G2H2I4A4B4C4D4E···4L7A7B7C14A···14U14V···14AG28A···28X
order12···22244444···477714···1414···1428···28
size11···144444428···282222···24···44···4

82 irreducible representations

dim111112222222224
type+++++++++++-
imageC1C2C2C2C2D4D4D7C4○D4D14D14C7⋊D4D28C4○D28D4⋊2D7
kernelC24.10D14C14.C42C2×C4⋊Dic7C2×C23.D7C14×C22⋊C4C2×C28C22×C14C2×C22⋊C4C2×C14C22×C4C24C2×C4C23C22C22
# reps13121223106312121212

Matrix representation of C24.10D14 ►in GL6(𝔽29)

2800000
0280000
001000
0002800
000010
00001928
,
100000
010000
0028000
0002800
0000280
0000028
,
100000
010000
001000
000100
0000280
0000028
,
300000
0100000
007000
0002500
000016
0000028
,
0100000
300000
0002500
007000
0000170
0000017

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,19,0,0,0,0,0,28],[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],[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],[3,0,0,0,0,0,0,10,0,0,0,0,0,0,7,0,0,0,0,0,0,25,0,0,0,0,0,0,1,0,0,0,0,0,6,28],[0,3,0,0,0,0,10,0,0,0,0,0,0,0,0,7,0,0,0,0,25,0,0,0,0,0,0,0,17,0,0,0,0,0,0,17] >;
 

C24.10D14 in GAP, Magma, Sage, TeX 

C_2^4._{10}D_{14}
 
% in TeX
 
G:=Group("C2^4.10D14");
 
// GroupNames label
 
G:=SmallGroup(448,487);
 
// by ID
 
G=gap.SmallGroup(448,487);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,120,254,387,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^28=1,e^2=c,a*b=b*a,d*a*d^-1=a*c=c*a,e*a*e^-1=a*b*c,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

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×
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