Copied to
clipboard

G = C23.11D30order 480 = 25·3·5

6th non-split extension by C23 of D30 acting via D30/C15=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C23.11D30, Dic15.20D4, (C2×C4).8D30, C22⋊C45D15, C6.101(D4×D5), (C2×C20).34D6, C2.10(D4×D15), D303C46C2, (C2×Dic30)⋊6C2, (C2×C12).34D10, C30.309(C2×D4), C10.103(S3×D4), (C4×Dic15)⋊18C2, C6.98(C4○D20), C30.38D45C2, C1519(C4.4D4), (C22×C6).60D10, (C22×C10).75D6, C10.98(C4○D12), C30.171(C4○D4), C6.93(D42D5), C2.9(D42D15), (C2×C60).175C22, (C2×C30).282C23, C35(Dic5.5D4), C55(C23.11D6), C10.93(D42S3), (C22×C30).16C22, C2.12(D6011C2), (C2×Dic15).8C22, (C22×D15).5C22, C22.44(C22×D15), (C5×C22⋊C4)⋊7S3, (C3×C22⋊C4)⋊7D5, (C15×C22⋊C4)⋊9C2, (C2×C157D4).4C2, (C2×C6).278(C22×D5), (C2×C10).277(C22×S3), SmallGroup(480,850)

Series: Derived Chief Lower central Upper central

C1C2×C30 — C23.11D30
C1C5C15C30C2×C30C22×D15D303C4 — C23.11D30
C15C2×C30 — C23.11D30
C1C22C22⋊C4

Generators and relations for C23.11D30
 G = < a,b,c,d,e | a2=b2=c2=1, d30=b, e2=cb=bc, eae-1=ab=ba, dad-1=ac=ca, bd=db, be=eb, cd=dc, ce=ec, ede-1=cd29 >

Subgroups: 932 in 152 conjugacy classes, 49 normal (47 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×6], C22, C22 [×6], C5, S3, C6 [×3], C6, C2×C4 [×2], C2×C4 [×3], D4 [×2], Q8 [×2], C23, C23, D5, C10 [×3], C10, Dic3 [×4], C12 [×2], D6 [×3], C2×C6, C2×C6 [×3], C15, C42, C22⋊C4, C22⋊C4 [×3], C2×D4, C2×Q8, Dic5 [×4], C20 [×2], D10 [×3], C2×C10, C2×C10 [×3], Dic6 [×2], C2×Dic3 [×3], C3⋊D4 [×2], C2×C12 [×2], C22×S3, C22×C6, D15, C30 [×3], C30, C4.4D4, Dic10 [×2], C2×Dic5 [×3], C5⋊D4 [×2], C2×C20 [×2], C22×D5, C22×C10, C4×Dic3, D6⋊C4 [×2], C6.D4, C3×C22⋊C4, C2×Dic6, C2×C3⋊D4, Dic15 [×2], Dic15 [×2], C60 [×2], D30 [×3], C2×C30, C2×C30 [×3], C4×Dic5, D10⋊C4 [×2], C23.D5, C5×C22⋊C4, C2×Dic10, C2×C5⋊D4, C23.11D6, Dic30 [×2], C2×Dic15 [×3], C157D4 [×2], C2×C60 [×2], C22×D15, C22×C30, Dic5.5D4, C4×Dic15, D303C4 [×2], C30.38D4, C15×C22⋊C4, C2×Dic30, C2×C157D4, C23.11D30
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], C22×S3, D15, C4.4D4, C22×D5, C4○D12, S3×D4, D42S3, D30 [×3], C4○D20, D4×D5, D42D5, C23.11D6, C22×D15, Dic5.5D4, D6011C2, D4×D15, D42D15, C23.11D30

Smallest permutation representation of C23.11D30
On 240 points
Generators in S240
(1 210)(2 129)(3 212)(4 131)(5 214)(6 133)(7 216)(8 135)(9 218)(10 137)(11 220)(12 139)(13 222)(14 141)(15 224)(16 143)(17 226)(18 145)(19 228)(20 147)(21 230)(22 149)(23 232)(24 151)(25 234)(26 153)(27 236)(28 155)(29 238)(30 157)(31 240)(32 159)(33 182)(34 161)(35 184)(36 163)(37 186)(38 165)(39 188)(40 167)(41 190)(42 169)(43 192)(44 171)(45 194)(46 173)(47 196)(48 175)(49 198)(50 177)(51 200)(52 179)(53 202)(54 121)(55 204)(56 123)(57 206)(58 125)(59 208)(60 127)(61 237)(62 156)(63 239)(64 158)(65 181)(66 160)(67 183)(68 162)(69 185)(70 164)(71 187)(72 166)(73 189)(74 168)(75 191)(76 170)(77 193)(78 172)(79 195)(80 174)(81 197)(82 176)(83 199)(84 178)(85 201)(86 180)(87 203)(88 122)(89 205)(90 124)(91 207)(92 126)(93 209)(94 128)(95 211)(96 130)(97 213)(98 132)(99 215)(100 134)(101 217)(102 136)(103 219)(104 138)(105 221)(106 140)(107 223)(108 142)(109 225)(110 144)(111 227)(112 146)(113 229)(114 148)(115 231)(116 150)(117 233)(118 152)(119 235)(120 154)
(1 31)(2 32)(3 33)(4 34)(5 35)(6 36)(7 37)(8 38)(9 39)(10 40)(11 41)(12 42)(13 43)(14 44)(15 45)(16 46)(17 47)(18 48)(19 49)(20 50)(21 51)(22 52)(23 53)(24 54)(25 55)(26 56)(27 57)(28 58)(29 59)(30 60)(61 91)(62 92)(63 93)(64 94)(65 95)(66 96)(67 97)(68 98)(69 99)(70 100)(71 101)(72 102)(73 103)(74 104)(75 105)(76 106)(77 107)(78 108)(79 109)(80 110)(81 111)(82 112)(83 113)(84 114)(85 115)(86 116)(87 117)(88 118)(89 119)(90 120)(121 151)(122 152)(123 153)(124 154)(125 155)(126 156)(127 157)(128 158)(129 159)(130 160)(131 161)(132 162)(133 163)(134 164)(135 165)(136 166)(137 167)(138 168)(139 169)(140 170)(141 171)(142 172)(143 173)(144 174)(145 175)(146 176)(147 177)(148 178)(149 179)(150 180)(181 211)(182 212)(183 213)(184 214)(185 215)(186 216)(187 217)(188 218)(189 219)(190 220)(191 221)(192 222)(193 223)(194 224)(195 225)(196 226)(197 227)(198 228)(199 229)(200 230)(201 231)(202 232)(203 233)(204 234)(205 235)(206 236)(207 237)(208 238)(209 239)(210 240)
(1 94)(2 95)(3 96)(4 97)(5 98)(6 99)(7 100)(8 101)(9 102)(10 103)(11 104)(12 105)(13 106)(14 107)(15 108)(16 109)(17 110)(18 111)(19 112)(20 113)(21 114)(22 115)(23 116)(24 117)(25 118)(26 119)(27 120)(28 61)(29 62)(30 63)(31 64)(32 65)(33 66)(34 67)(35 68)(36 69)(37 70)(38 71)(39 72)(40 73)(41 74)(42 75)(43 76)(44 77)(45 78)(46 79)(47 80)(48 81)(49 82)(50 83)(51 84)(52 85)(53 86)(54 87)(55 88)(56 89)(57 90)(58 91)(59 92)(60 93)(121 203)(122 204)(123 205)(124 206)(125 207)(126 208)(127 209)(128 210)(129 211)(130 212)(131 213)(132 214)(133 215)(134 216)(135 217)(136 218)(137 219)(138 220)(139 221)(140 222)(141 223)(142 224)(143 225)(144 226)(145 227)(146 228)(147 229)(148 230)(149 231)(150 232)(151 233)(152 234)(153 235)(154 236)(155 237)(156 238)(157 239)(158 240)(159 181)(160 182)(161 183)(162 184)(163 185)(164 186)(165 187)(166 188)(167 189)(168 190)(169 191)(170 192)(171 193)(172 194)(173 195)(174 196)(175 197)(176 198)(177 199)(178 200)(179 201)(180 202)
(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 30 64 93)(2 92 65 29)(3 28 66 91)(4 90 67 27)(5 26 68 89)(6 88 69 25)(7 24 70 87)(8 86 71 23)(9 22 72 85)(10 84 73 21)(11 20 74 83)(12 82 75 19)(13 18 76 81)(14 80 77 17)(15 16 78 79)(31 60 94 63)(32 62 95 59)(33 58 96 61)(34 120 97 57)(35 56 98 119)(36 118 99 55)(37 54 100 117)(38 116 101 53)(39 52 102 115)(40 114 103 51)(41 50 104 113)(42 112 105 49)(43 48 106 111)(44 110 107 47)(45 46 108 109)(121 164 233 216)(122 215 234 163)(123 162 235 214)(124 213 236 161)(125 160 237 212)(126 211 238 159)(127 158 239 210)(128 209 240 157)(129 156 181 208)(130 207 182 155)(131 154 183 206)(132 205 184 153)(133 152 185 204)(134 203 186 151)(135 150 187 202)(136 201 188 149)(137 148 189 200)(138 199 190 147)(139 146 191 198)(140 197 192 145)(141 144 193 196)(142 195 194 143)(165 180 217 232)(166 231 218 179)(167 178 219 230)(168 229 220 177)(169 176 221 228)(170 227 222 175)(171 174 223 226)(172 225 224 173)

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

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

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

84 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F4G4H5A5B6A6B6C6D6E10A···10F10G10H10I10J12A12B12C12D15A15B15C15D20A···20H30A···30L30M···30T60A···60P
order122222344444444556666610···1010101010121212121515151520···2030···3030···3060···60
size11114602224303030306022222442···24444444422224···42···24···44···4

84 irreducible representations

dim111111122222222222222444444
type++++++++++++++++++-+-+-
imageC1C2C2C2C2C2C2S3D4D5D6D6C4○D4D10D10D15C4○D12D30D30C4○D20D6011C2S3×D4D42S3D4×D5D42D5D4×D15D42D15
kernelC23.11D30C4×Dic15D303C4C30.38D4C15×C22⋊C4C2×Dic30C2×C157D4C5×C22⋊C4Dic15C3×C22⋊C4C2×C20C22×C10C30C2×C12C22×C6C22⋊C4C10C2×C4C23C6C2C10C10C6C6C2C2
# reps1121111122214424484816112244

Matrix representation of C23.11D30 in GL6(𝔽61)

47440000
33140000
001000
000100
0000600
0000201
,
6000000
0600000
001000
000100
0000600
0000060
,
100000
010000
001000
000100
0000600
0000060
,
4110000
54110000
0006000
001100
0000606
0000201
,
5890000
2630000
0006000
0060000
0000155
0000060

G:=sub<GL(6,GF(61))| [47,33,0,0,0,0,44,14,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,20,0,0,0,0,0,1],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[4,54,0,0,0,0,11,11,0,0,0,0,0,0,0,1,0,0,0,0,60,1,0,0,0,0,0,0,60,20,0,0,0,0,6,1],[58,26,0,0,0,0,9,3,0,0,0,0,0,0,0,60,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,55,60] >;

C23.11D30 in GAP, Magma, Sage, TeX

C_2^3._{11}D_{30}
% in TeX

G:=Group("C2^3.11D30");
// GroupNames label

G:=SmallGroup(480,850);
// by ID

G=gap.SmallGroup(480,850);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,253,64,590,219,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^30=b,e^2=c*b=b*c,e*a*e^-1=a*b=b*a,d*a*d^-1=a*c=c*a,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=c*d^29>;
// generators/relations

׿
×
𝔽