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G = C3×C23.18D10order 480 = 25·3·5

Direct product of C3 and C23.18D10

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C3×C23.18D10, (C6×D4).11D5, C10.51(C6×D4), (C2×C30).84D4, C23.D58C6, (D4×C10).10C6, (D4×C30).22C2, C30.405(C2×D4), C23.22(C6×D5), (C22×C6).7D10, C10.D414C6, (C2×C12).240D10, (C22×Dic5)⋊8C6, C30.238(C4○D4), (C2×C60).423C22, (C2×C30).367C23, C6.120(D42D5), C1538(C22.D4), (C22×C30).104C22, (C6×Dic5).250C22, (C2×C6×Dic5)⋊16C2, (C2×D4).5(C3×D5), (C2×C4).14(C6×D5), (C2×C10).7(C3×D4), C2.11(C6×C5⋊D4), C22.57(D5×C2×C6), (C2×C20).61(C2×C6), C10.28(C3×C4○D4), C6.132(C2×C5⋊D4), C22.4(C3×C5⋊D4), C55(C3×C22.D4), C2.15(C3×D42D5), (C2×C6).40(C5⋊D4), (C3×C23.D5)⋊24C2, (C3×C10.D4)⋊36C2, (C2×C10).50(C22×C6), (C22×C10).23(C2×C6), (C2×Dic5).39(C2×C6), (C2×C6).363(C22×D5), SmallGroup(480,728)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C3×C23.18D10
C1C5C10C2×C10C2×C30C6×Dic5C2×C6×Dic5 — C3×C23.18D10
C5C2×C10 — C3×C23.18D10
C1C2×C6C6×D4

Generators and relations for C3×C23.18D10
 G = < a,b,c,d,e,f | a3=b2=c2=d2=e10=1, f2=dc=cd, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, ebe-1=fbf-1=bd=db, ce=ec, cf=fc, de=ed, df=fd, fef-1=ce-1 >

Subgroups: 416 in 156 conjugacy classes, 66 normal (34 characteristic)
C1, C2, C2 [×2], C2 [×3], C3, C4 [×5], C22, C22 [×2], C22 [×5], C5, C6, C6 [×2], C6 [×3], C2×C4, C2×C4 [×6], D4 [×2], C23 [×2], C10, C10 [×2], C10 [×3], C12 [×5], C2×C6, C2×C6 [×2], C2×C6 [×5], C15, C22⋊C4 [×3], C4⋊C4 [×2], C22×C4, C2×D4, Dic5 [×4], C20, C2×C10, C2×C10 [×2], C2×C10 [×5], C2×C12, C2×C12 [×6], C3×D4 [×2], C22×C6 [×2], C30, C30 [×2], C30 [×3], C22.D4, C2×Dic5 [×4], C2×Dic5 [×2], C2×C20, C5×D4 [×2], C22×C10 [×2], C3×C22⋊C4 [×3], C3×C4⋊C4 [×2], C22×C12, C6×D4, C3×Dic5 [×4], C60, C2×C30, C2×C30 [×2], C2×C30 [×5], C10.D4 [×2], C23.D5, C23.D5 [×2], C22×Dic5, D4×C10, C3×C22.D4, C6×Dic5 [×4], C6×Dic5 [×2], C2×C60, D4×C15 [×2], C22×C30 [×2], C23.18D10, C3×C10.D4 [×2], C3×C23.D5, C3×C23.D5 [×2], C2×C6×Dic5, D4×C30, C3×C23.18D10
Quotients: C1, C2 [×7], C3, C22 [×7], C6 [×7], D4 [×2], C23, D5, C2×C6 [×7], C2×D4, C4○D4 [×2], D10 [×3], C3×D4 [×2], C22×C6, C3×D5, C22.D4, C5⋊D4 [×2], C22×D5, C6×D4, C3×C4○D4 [×2], C6×D5 [×3], D42D5 [×2], C2×C5⋊D4, C3×C22.D4, C3×C5⋊D4 [×2], D5×C2×C6, C23.18D10, C3×D42D5 [×2], C6×C5⋊D4, C3×C23.18D10

Smallest permutation representation of C3×C23.18D10
On 240 points
Generators in S240
(1 31 21)(2 32 22)(3 33 23)(4 34 24)(5 35 25)(6 36 26)(7 37 27)(8 38 28)(9 39 29)(10 40 30)(11 81 71)(12 82 72)(13 83 73)(14 84 74)(15 85 75)(16 86 76)(17 87 77)(18 88 78)(19 89 79)(20 90 80)(41 140 51)(42 131 52)(43 132 53)(44 133 54)(45 134 55)(46 135 56)(47 136 57)(48 137 58)(49 138 59)(50 139 60)(61 164 174)(62 165 175)(63 166 176)(64 167 177)(65 168 178)(66 169 179)(67 170 180)(68 161 171)(69 162 172)(70 163 173)(91 111 101)(92 112 102)(93 113 103)(94 114 104)(95 115 105)(96 116 106)(97 117 107)(98 118 108)(99 119 109)(100 120 110)(121 209 199)(122 210 200)(123 201 191)(124 202 192)(125 203 193)(126 204 194)(127 205 195)(128 206 196)(129 207 197)(130 208 198)(141 151 189)(142 152 190)(143 153 181)(144 154 182)(145 155 183)(146 156 184)(147 157 185)(148 158 186)(149 159 187)(150 160 188)(211 231 221)(212 232 222)(213 233 223)(214 234 224)(215 235 225)(216 236 226)(217 237 227)(218 238 228)(219 239 229)(220 240 230)
(2 98)(4 100)(6 92)(8 94)(10 96)(12 133)(14 135)(16 137)(18 139)(20 131)(22 108)(24 110)(26 102)(28 104)(30 106)(32 118)(34 120)(36 112)(38 114)(40 116)(42 80)(44 72)(46 74)(48 76)(50 78)(52 90)(54 82)(56 84)(58 86)(60 88)(62 187)(64 189)(66 181)(68 183)(70 185)(122 216)(124 218)(126 220)(128 212)(130 214)(141 167)(143 169)(145 161)(147 163)(149 165)(151 177)(153 179)(155 171)(157 173)(159 175)(192 228)(194 230)(196 222)(198 224)(200 226)(202 238)(204 240)(206 232)(208 234)(210 236)
(1 73)(2 74)(3 75)(4 76)(5 77)(6 78)(7 79)(8 80)(9 71)(10 72)(11 39)(12 40)(13 31)(14 32)(15 33)(16 34)(17 35)(18 36)(19 37)(20 38)(21 83)(22 84)(23 85)(24 86)(25 87)(26 88)(27 89)(28 90)(29 81)(30 82)(41 93)(42 94)(43 95)(44 96)(45 97)(46 98)(47 99)(48 100)(49 91)(50 92)(51 103)(52 104)(53 105)(54 106)(55 107)(56 108)(57 109)(58 110)(59 101)(60 102)(61 237)(62 238)(63 239)(64 240)(65 231)(66 232)(67 233)(68 234)(69 235)(70 236)(111 138)(112 139)(113 140)(114 131)(115 132)(116 133)(117 134)(118 135)(119 136)(120 137)(121 156)(122 157)(123 158)(124 159)(125 160)(126 151)(127 152)(128 153)(129 154)(130 155)(141 194)(142 195)(143 196)(144 197)(145 198)(146 199)(147 200)(148 191)(149 192)(150 193)(161 224)(162 225)(163 226)(164 227)(165 228)(166 229)(167 230)(168 221)(169 222)(170 223)(171 214)(172 215)(173 216)(174 217)(175 218)(176 219)(177 220)(178 211)(179 212)(180 213)(181 206)(182 207)(183 208)(184 209)(185 210)(186 201)(187 202)(188 203)(189 204)(190 205)
(1 97)(2 98)(3 99)(4 100)(5 91)(6 92)(7 93)(8 94)(9 95)(10 96)(11 132)(12 133)(13 134)(14 135)(15 136)(16 137)(17 138)(18 139)(19 140)(20 131)(21 107)(22 108)(23 109)(24 110)(25 101)(26 102)(27 103)(28 104)(29 105)(30 106)(31 117)(32 118)(33 119)(34 120)(35 111)(36 112)(37 113)(38 114)(39 115)(40 116)(41 79)(42 80)(43 71)(44 72)(45 73)(46 74)(47 75)(48 76)(49 77)(50 78)(51 89)(52 90)(53 81)(54 82)(55 83)(56 84)(57 85)(58 86)(59 87)(60 88)(61 186)(62 187)(63 188)(64 189)(65 190)(66 181)(67 182)(68 183)(69 184)(70 185)(121 215)(122 216)(123 217)(124 218)(125 219)(126 220)(127 211)(128 212)(129 213)(130 214)(141 167)(142 168)(143 169)(144 170)(145 161)(146 162)(147 163)(148 164)(149 165)(150 166)(151 177)(152 178)(153 179)(154 180)(155 171)(156 172)(157 173)(158 174)(159 175)(160 176)(191 227)(192 228)(193 229)(194 230)(195 221)(196 222)(197 223)(198 224)(199 225)(200 226)(201 237)(202 238)(203 239)(204 240)(205 231)(206 232)(207 233)(208 234)(209 235)(210 236)
(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)(221 222 223 224 225 226 227 228 229 230)(231 232 233 234 235 236 237 238 239 240)
(1 179 45 128)(2 211 46 152)(3 177 47 126)(4 219 48 160)(5 175 49 124)(6 217 50 158)(7 173 41 122)(8 215 42 156)(9 171 43 130)(10 213 44 154)(11 234 115 183)(12 67 116 207)(13 232 117 181)(14 65 118 205)(15 240 119 189)(16 63 120 203)(17 238 111 187)(18 61 112 201)(19 236 113 185)(20 69 114 209)(21 169 55 196)(22 221 56 142)(23 167 57 194)(24 229 58 150)(25 165 59 192)(26 227 60 148)(27 163 51 200)(28 225 52 146)(29 161 53 198)(30 223 54 144)(31 66 134 206)(32 231 135 190)(33 64 136 204)(34 239 137 188)(35 62 138 202)(36 237 139 186)(37 70 140 210)(38 235 131 184)(39 68 132 208)(40 233 133 182)(71 214 95 155)(72 180 96 129)(73 212 97 153)(74 178 98 127)(75 220 99 151)(76 176 100 125)(77 218 91 159)(78 174 92 123)(79 216 93 157)(80 172 94 121)(81 224 105 145)(82 170 106 197)(83 222 107 143)(84 168 108 195)(85 230 109 141)(86 166 110 193)(87 228 101 149)(88 164 102 191)(89 226 103 147)(90 162 104 199)

G:=sub<Sym(240)| (1,31,21)(2,32,22)(3,33,23)(4,34,24)(5,35,25)(6,36,26)(7,37,27)(8,38,28)(9,39,29)(10,40,30)(11,81,71)(12,82,72)(13,83,73)(14,84,74)(15,85,75)(16,86,76)(17,87,77)(18,88,78)(19,89,79)(20,90,80)(41,140,51)(42,131,52)(43,132,53)(44,133,54)(45,134,55)(46,135,56)(47,136,57)(48,137,58)(49,138,59)(50,139,60)(61,164,174)(62,165,175)(63,166,176)(64,167,177)(65,168,178)(66,169,179)(67,170,180)(68,161,171)(69,162,172)(70,163,173)(91,111,101)(92,112,102)(93,113,103)(94,114,104)(95,115,105)(96,116,106)(97,117,107)(98,118,108)(99,119,109)(100,120,110)(121,209,199)(122,210,200)(123,201,191)(124,202,192)(125,203,193)(126,204,194)(127,205,195)(128,206,196)(129,207,197)(130,208,198)(141,151,189)(142,152,190)(143,153,181)(144,154,182)(145,155,183)(146,156,184)(147,157,185)(148,158,186)(149,159,187)(150,160,188)(211,231,221)(212,232,222)(213,233,223)(214,234,224)(215,235,225)(216,236,226)(217,237,227)(218,238,228)(219,239,229)(220,240,230), (2,98)(4,100)(6,92)(8,94)(10,96)(12,133)(14,135)(16,137)(18,139)(20,131)(22,108)(24,110)(26,102)(28,104)(30,106)(32,118)(34,120)(36,112)(38,114)(40,116)(42,80)(44,72)(46,74)(48,76)(50,78)(52,90)(54,82)(56,84)(58,86)(60,88)(62,187)(64,189)(66,181)(68,183)(70,185)(122,216)(124,218)(126,220)(128,212)(130,214)(141,167)(143,169)(145,161)(147,163)(149,165)(151,177)(153,179)(155,171)(157,173)(159,175)(192,228)(194,230)(196,222)(198,224)(200,226)(202,238)(204,240)(206,232)(208,234)(210,236), (1,73)(2,74)(3,75)(4,76)(5,77)(6,78)(7,79)(8,80)(9,71)(10,72)(11,39)(12,40)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,83)(22,84)(23,85)(24,86)(25,87)(26,88)(27,89)(28,90)(29,81)(30,82)(41,93)(42,94)(43,95)(44,96)(45,97)(46,98)(47,99)(48,100)(49,91)(50,92)(51,103)(52,104)(53,105)(54,106)(55,107)(56,108)(57,109)(58,110)(59,101)(60,102)(61,237)(62,238)(63,239)(64,240)(65,231)(66,232)(67,233)(68,234)(69,235)(70,236)(111,138)(112,139)(113,140)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(120,137)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(141,194)(142,195)(143,196)(144,197)(145,198)(146,199)(147,200)(148,191)(149,192)(150,193)(161,224)(162,225)(163,226)(164,227)(165,228)(166,229)(167,230)(168,221)(169,222)(170,223)(171,214)(172,215)(173,216)(174,217)(175,218)(176,219)(177,220)(178,211)(179,212)(180,213)(181,206)(182,207)(183,208)(184,209)(185,210)(186,201)(187,202)(188,203)(189,204)(190,205), (1,97)(2,98)(3,99)(4,100)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,132)(12,133)(13,134)(14,135)(15,136)(16,137)(17,138)(18,139)(19,140)(20,131)(21,107)(22,108)(23,109)(24,110)(25,101)(26,102)(27,103)(28,104)(29,105)(30,106)(31,117)(32,118)(33,119)(34,120)(35,111)(36,112)(37,113)(38,114)(39,115)(40,116)(41,79)(42,80)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,89)(52,90)(53,81)(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,186)(62,187)(63,188)(64,189)(65,190)(66,181)(67,182)(68,183)(69,184)(70,185)(121,215)(122,216)(123,217)(124,218)(125,219)(126,220)(127,211)(128,212)(129,213)(130,214)(141,167)(142,168)(143,169)(144,170)(145,161)(146,162)(147,163)(148,164)(149,165)(150,166)(151,177)(152,178)(153,179)(154,180)(155,171)(156,172)(157,173)(158,174)(159,175)(160,176)(191,227)(192,228)(193,229)(194,230)(195,221)(196,222)(197,223)(198,224)(199,225)(200,226)(201,237)(202,238)(203,239)(204,240)(205,231)(206,232)(207,233)(208,234)(209,235)(210,236), (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)(221,222,223,224,225,226,227,228,229,230)(231,232,233,234,235,236,237,238,239,240), (1,179,45,128)(2,211,46,152)(3,177,47,126)(4,219,48,160)(5,175,49,124)(6,217,50,158)(7,173,41,122)(8,215,42,156)(9,171,43,130)(10,213,44,154)(11,234,115,183)(12,67,116,207)(13,232,117,181)(14,65,118,205)(15,240,119,189)(16,63,120,203)(17,238,111,187)(18,61,112,201)(19,236,113,185)(20,69,114,209)(21,169,55,196)(22,221,56,142)(23,167,57,194)(24,229,58,150)(25,165,59,192)(26,227,60,148)(27,163,51,200)(28,225,52,146)(29,161,53,198)(30,223,54,144)(31,66,134,206)(32,231,135,190)(33,64,136,204)(34,239,137,188)(35,62,138,202)(36,237,139,186)(37,70,140,210)(38,235,131,184)(39,68,132,208)(40,233,133,182)(71,214,95,155)(72,180,96,129)(73,212,97,153)(74,178,98,127)(75,220,99,151)(76,176,100,125)(77,218,91,159)(78,174,92,123)(79,216,93,157)(80,172,94,121)(81,224,105,145)(82,170,106,197)(83,222,107,143)(84,168,108,195)(85,230,109,141)(86,166,110,193)(87,228,101,149)(88,164,102,191)(89,226,103,147)(90,162,104,199)>;

G:=Group( (1,31,21)(2,32,22)(3,33,23)(4,34,24)(5,35,25)(6,36,26)(7,37,27)(8,38,28)(9,39,29)(10,40,30)(11,81,71)(12,82,72)(13,83,73)(14,84,74)(15,85,75)(16,86,76)(17,87,77)(18,88,78)(19,89,79)(20,90,80)(41,140,51)(42,131,52)(43,132,53)(44,133,54)(45,134,55)(46,135,56)(47,136,57)(48,137,58)(49,138,59)(50,139,60)(61,164,174)(62,165,175)(63,166,176)(64,167,177)(65,168,178)(66,169,179)(67,170,180)(68,161,171)(69,162,172)(70,163,173)(91,111,101)(92,112,102)(93,113,103)(94,114,104)(95,115,105)(96,116,106)(97,117,107)(98,118,108)(99,119,109)(100,120,110)(121,209,199)(122,210,200)(123,201,191)(124,202,192)(125,203,193)(126,204,194)(127,205,195)(128,206,196)(129,207,197)(130,208,198)(141,151,189)(142,152,190)(143,153,181)(144,154,182)(145,155,183)(146,156,184)(147,157,185)(148,158,186)(149,159,187)(150,160,188)(211,231,221)(212,232,222)(213,233,223)(214,234,224)(215,235,225)(216,236,226)(217,237,227)(218,238,228)(219,239,229)(220,240,230), (2,98)(4,100)(6,92)(8,94)(10,96)(12,133)(14,135)(16,137)(18,139)(20,131)(22,108)(24,110)(26,102)(28,104)(30,106)(32,118)(34,120)(36,112)(38,114)(40,116)(42,80)(44,72)(46,74)(48,76)(50,78)(52,90)(54,82)(56,84)(58,86)(60,88)(62,187)(64,189)(66,181)(68,183)(70,185)(122,216)(124,218)(126,220)(128,212)(130,214)(141,167)(143,169)(145,161)(147,163)(149,165)(151,177)(153,179)(155,171)(157,173)(159,175)(192,228)(194,230)(196,222)(198,224)(200,226)(202,238)(204,240)(206,232)(208,234)(210,236), (1,73)(2,74)(3,75)(4,76)(5,77)(6,78)(7,79)(8,80)(9,71)(10,72)(11,39)(12,40)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(19,37)(20,38)(21,83)(22,84)(23,85)(24,86)(25,87)(26,88)(27,89)(28,90)(29,81)(30,82)(41,93)(42,94)(43,95)(44,96)(45,97)(46,98)(47,99)(48,100)(49,91)(50,92)(51,103)(52,104)(53,105)(54,106)(55,107)(56,108)(57,109)(58,110)(59,101)(60,102)(61,237)(62,238)(63,239)(64,240)(65,231)(66,232)(67,233)(68,234)(69,235)(70,236)(111,138)(112,139)(113,140)(114,131)(115,132)(116,133)(117,134)(118,135)(119,136)(120,137)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(141,194)(142,195)(143,196)(144,197)(145,198)(146,199)(147,200)(148,191)(149,192)(150,193)(161,224)(162,225)(163,226)(164,227)(165,228)(166,229)(167,230)(168,221)(169,222)(170,223)(171,214)(172,215)(173,216)(174,217)(175,218)(176,219)(177,220)(178,211)(179,212)(180,213)(181,206)(182,207)(183,208)(184,209)(185,210)(186,201)(187,202)(188,203)(189,204)(190,205), (1,97)(2,98)(3,99)(4,100)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,132)(12,133)(13,134)(14,135)(15,136)(16,137)(17,138)(18,139)(19,140)(20,131)(21,107)(22,108)(23,109)(24,110)(25,101)(26,102)(27,103)(28,104)(29,105)(30,106)(31,117)(32,118)(33,119)(34,120)(35,111)(36,112)(37,113)(38,114)(39,115)(40,116)(41,79)(42,80)(43,71)(44,72)(45,73)(46,74)(47,75)(48,76)(49,77)(50,78)(51,89)(52,90)(53,81)(54,82)(55,83)(56,84)(57,85)(58,86)(59,87)(60,88)(61,186)(62,187)(63,188)(64,189)(65,190)(66,181)(67,182)(68,183)(69,184)(70,185)(121,215)(122,216)(123,217)(124,218)(125,219)(126,220)(127,211)(128,212)(129,213)(130,214)(141,167)(142,168)(143,169)(144,170)(145,161)(146,162)(147,163)(148,164)(149,165)(150,166)(151,177)(152,178)(153,179)(154,180)(155,171)(156,172)(157,173)(158,174)(159,175)(160,176)(191,227)(192,228)(193,229)(194,230)(195,221)(196,222)(197,223)(198,224)(199,225)(200,226)(201,237)(202,238)(203,239)(204,240)(205,231)(206,232)(207,233)(208,234)(209,235)(210,236), (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)(221,222,223,224,225,226,227,228,229,230)(231,232,233,234,235,236,237,238,239,240), (1,179,45,128)(2,211,46,152)(3,177,47,126)(4,219,48,160)(5,175,49,124)(6,217,50,158)(7,173,41,122)(8,215,42,156)(9,171,43,130)(10,213,44,154)(11,234,115,183)(12,67,116,207)(13,232,117,181)(14,65,118,205)(15,240,119,189)(16,63,120,203)(17,238,111,187)(18,61,112,201)(19,236,113,185)(20,69,114,209)(21,169,55,196)(22,221,56,142)(23,167,57,194)(24,229,58,150)(25,165,59,192)(26,227,60,148)(27,163,51,200)(28,225,52,146)(29,161,53,198)(30,223,54,144)(31,66,134,206)(32,231,135,190)(33,64,136,204)(34,239,137,188)(35,62,138,202)(36,237,139,186)(37,70,140,210)(38,235,131,184)(39,68,132,208)(40,233,133,182)(71,214,95,155)(72,180,96,129)(73,212,97,153)(74,178,98,127)(75,220,99,151)(76,176,100,125)(77,218,91,159)(78,174,92,123)(79,216,93,157)(80,172,94,121)(81,224,105,145)(82,170,106,197)(83,222,107,143)(84,168,108,195)(85,230,109,141)(86,166,110,193)(87,228,101,149)(88,164,102,191)(89,226,103,147)(90,162,104,199) );

G=PermutationGroup([(1,31,21),(2,32,22),(3,33,23),(4,34,24),(5,35,25),(6,36,26),(7,37,27),(8,38,28),(9,39,29),(10,40,30),(11,81,71),(12,82,72),(13,83,73),(14,84,74),(15,85,75),(16,86,76),(17,87,77),(18,88,78),(19,89,79),(20,90,80),(41,140,51),(42,131,52),(43,132,53),(44,133,54),(45,134,55),(46,135,56),(47,136,57),(48,137,58),(49,138,59),(50,139,60),(61,164,174),(62,165,175),(63,166,176),(64,167,177),(65,168,178),(66,169,179),(67,170,180),(68,161,171),(69,162,172),(70,163,173),(91,111,101),(92,112,102),(93,113,103),(94,114,104),(95,115,105),(96,116,106),(97,117,107),(98,118,108),(99,119,109),(100,120,110),(121,209,199),(122,210,200),(123,201,191),(124,202,192),(125,203,193),(126,204,194),(127,205,195),(128,206,196),(129,207,197),(130,208,198),(141,151,189),(142,152,190),(143,153,181),(144,154,182),(145,155,183),(146,156,184),(147,157,185),(148,158,186),(149,159,187),(150,160,188),(211,231,221),(212,232,222),(213,233,223),(214,234,224),(215,235,225),(216,236,226),(217,237,227),(218,238,228),(219,239,229),(220,240,230)], [(2,98),(4,100),(6,92),(8,94),(10,96),(12,133),(14,135),(16,137),(18,139),(20,131),(22,108),(24,110),(26,102),(28,104),(30,106),(32,118),(34,120),(36,112),(38,114),(40,116),(42,80),(44,72),(46,74),(48,76),(50,78),(52,90),(54,82),(56,84),(58,86),(60,88),(62,187),(64,189),(66,181),(68,183),(70,185),(122,216),(124,218),(126,220),(128,212),(130,214),(141,167),(143,169),(145,161),(147,163),(149,165),(151,177),(153,179),(155,171),(157,173),(159,175),(192,228),(194,230),(196,222),(198,224),(200,226),(202,238),(204,240),(206,232),(208,234),(210,236)], [(1,73),(2,74),(3,75),(4,76),(5,77),(6,78),(7,79),(8,80),(9,71),(10,72),(11,39),(12,40),(13,31),(14,32),(15,33),(16,34),(17,35),(18,36),(19,37),(20,38),(21,83),(22,84),(23,85),(24,86),(25,87),(26,88),(27,89),(28,90),(29,81),(30,82),(41,93),(42,94),(43,95),(44,96),(45,97),(46,98),(47,99),(48,100),(49,91),(50,92),(51,103),(52,104),(53,105),(54,106),(55,107),(56,108),(57,109),(58,110),(59,101),(60,102),(61,237),(62,238),(63,239),(64,240),(65,231),(66,232),(67,233),(68,234),(69,235),(70,236),(111,138),(112,139),(113,140),(114,131),(115,132),(116,133),(117,134),(118,135),(119,136),(120,137),(121,156),(122,157),(123,158),(124,159),(125,160),(126,151),(127,152),(128,153),(129,154),(130,155),(141,194),(142,195),(143,196),(144,197),(145,198),(146,199),(147,200),(148,191),(149,192),(150,193),(161,224),(162,225),(163,226),(164,227),(165,228),(166,229),(167,230),(168,221),(169,222),(170,223),(171,214),(172,215),(173,216),(174,217),(175,218),(176,219),(177,220),(178,211),(179,212),(180,213),(181,206),(182,207),(183,208),(184,209),(185,210),(186,201),(187,202),(188,203),(189,204),(190,205)], [(1,97),(2,98),(3,99),(4,100),(5,91),(6,92),(7,93),(8,94),(9,95),(10,96),(11,132),(12,133),(13,134),(14,135),(15,136),(16,137),(17,138),(18,139),(19,140),(20,131),(21,107),(22,108),(23,109),(24,110),(25,101),(26,102),(27,103),(28,104),(29,105),(30,106),(31,117),(32,118),(33,119),(34,120),(35,111),(36,112),(37,113),(38,114),(39,115),(40,116),(41,79),(42,80),(43,71),(44,72),(45,73),(46,74),(47,75),(48,76),(49,77),(50,78),(51,89),(52,90),(53,81),(54,82),(55,83),(56,84),(57,85),(58,86),(59,87),(60,88),(61,186),(62,187),(63,188),(64,189),(65,190),(66,181),(67,182),(68,183),(69,184),(70,185),(121,215),(122,216),(123,217),(124,218),(125,219),(126,220),(127,211),(128,212),(129,213),(130,214),(141,167),(142,168),(143,169),(144,170),(145,161),(146,162),(147,163),(148,164),(149,165),(150,166),(151,177),(152,178),(153,179),(154,180),(155,171),(156,172),(157,173),(158,174),(159,175),(160,176),(191,227),(192,228),(193,229),(194,230),(195,221),(196,222),(197,223),(198,224),(199,225),(200,226),(201,237),(202,238),(203,239),(204,240),(205,231),(206,232),(207,233),(208,234),(209,235),(210,236)], [(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),(221,222,223,224,225,226,227,228,229,230),(231,232,233,234,235,236,237,238,239,240)], [(1,179,45,128),(2,211,46,152),(3,177,47,126),(4,219,48,160),(5,175,49,124),(6,217,50,158),(7,173,41,122),(8,215,42,156),(9,171,43,130),(10,213,44,154),(11,234,115,183),(12,67,116,207),(13,232,117,181),(14,65,118,205),(15,240,119,189),(16,63,120,203),(17,238,111,187),(18,61,112,201),(19,236,113,185),(20,69,114,209),(21,169,55,196),(22,221,56,142),(23,167,57,194),(24,229,58,150),(25,165,59,192),(26,227,60,148),(27,163,51,200),(28,225,52,146),(29,161,53,198),(30,223,54,144),(31,66,134,206),(32,231,135,190),(33,64,136,204),(34,239,137,188),(35,62,138,202),(36,237,139,186),(37,70,140,210),(38,235,131,184),(39,68,132,208),(40,233,133,182),(71,214,95,155),(72,180,96,129),(73,212,97,153),(74,178,98,127),(75,220,99,151),(76,176,100,125),(77,218,91,159),(78,174,92,123),(79,216,93,157),(80,172,94,121),(81,224,105,145),(82,170,106,197),(83,222,107,143),(84,168,108,195),(85,230,109,141),(86,166,110,193),(87,228,101,149),(88,164,102,191),(89,226,103,147),(90,162,104,199)])

102 conjugacy classes

class 1 2A2B2C2D2E2F3A3B4A4B4C4D4E4F4G5A5B6A···6F6G6H6I6J6K6L10A···10F10G···10N12A12B12C···12J12K12L12M12N15A15B15C15D20A20B20C20D30A···30L30M···30AB60A···60H
order1222222334444444556···666666610···1010···10121212···1212121212151515152020202030···3030···3060···60
size1111224114101010102020221···12222442···24···44410···1020202020222244442···24···44···4

102 irreducible representations

dim111111111122222222222244
type+++++++++-
imageC1C2C2C2C2C3C6C6C6C6D4D5C4○D4D10D10C3×D4C3×D5C5⋊D4C3×C4○D4C6×D5C6×D5C3×C5⋊D4D42D5C3×D42D5
kernelC3×C23.18D10C3×C10.D4C3×C23.D5C2×C6×Dic5D4×C30C23.18D10C10.D4C23.D5C22×Dic5D4×C10C2×C30C6×D4C30C2×C12C22×C6C2×C10C2×D4C2×C6C10C2×C4C23C22C6C2
# reps1231124622224244488481648

Matrix representation of C3×C23.18D10 in GL4(𝔽61) generated by

13000
01300
0010
0001
,
1000
0100
0010
00060
,
60000
06000
00600
00060
,
1000
0100
00600
00060
,
532200
94400
0001
0010
,
345800
402700
00050
00110
G:=sub<GL(4,GF(61))| [13,0,0,0,0,13,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,60],[60,0,0,0,0,60,0,0,0,0,60,0,0,0,0,60],[1,0,0,0,0,1,0,0,0,0,60,0,0,0,0,60],[53,9,0,0,22,44,0,0,0,0,0,1,0,0,1,0],[34,40,0,0,58,27,0,0,0,0,0,11,0,0,50,0] >;

C3×C23.18D10 in GAP, Magma, Sage, TeX

C_3\times C_2^3._{18}D_{10}
% in TeX

G:=Group("C3xC2^3.18D10");
// GroupNames label

G:=SmallGroup(480,728);
// by ID

G=gap.SmallGroup(480,728);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-2,-2,-5,336,590,555,18822]);
// Polycyclic

G:=Group<a,b,c,d,e,f|a^3=b^2=c^2=d^2=e^10=1,f^2=d*c=c*d,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,e*b*e^-1=f*b*f^-1=b*d=d*b,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=c*e^-1>;
// generators/relations

׿
×
𝔽