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G = C22×C157D4order 480 = 25·3·5

Direct product of C22 and C157D4

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

Aliases: C22×C157D4, C246D15, C235D30, D308C23, C30.68C24, Dic155C23, C3016(C2×D4), (C2×C30)⋊31D4, (C23×C6)⋊6D5, (C23×C30)⋊4C2, C1517(C22×D4), (C23×C10)⋊10S3, (C2×C30)⋊10C23, (C23×D15)⋊5C2, (C22×C10)⋊17D6, (C22×C6)⋊14D10, C6.68(C23×D5), C10.68(S3×C23), C2.15(C23×D15), C223(C22×D15), (C22×C30)⋊19C22, (C22×Dic15)⋊9C2, (C2×Dic15)⋊28C22, (C22×D15)⋊19C22, C64(C2×C5⋊D4), C104(C2×C3⋊D4), C34(C22×C5⋊D4), C54(C22×C3⋊D4), (C2×C6)⋊9(C22×D5), (C2×C6)⋊15(C5⋊D4), (C2×C10)⋊19(C3⋊D4), (C2×C10)⋊12(C22×S3), SmallGroup(480,1179)

Series: Derived Chief Lower central Upper central

C1C30 — C22×C157D4
C1C5C15C30D30C22×D15C23×D15 — C22×C157D4
C15C30 — C22×C157D4
C1C23C24

Generators and relations for C22×C157D4
 G = < a,b,c,d,e | a2=b2=c15=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, dcd-1=ece=c-1, ede=d-1 >

Subgroups: 2452 in 472 conjugacy classes, 159 normal (19 characteristic)
C1, C2, C2 [×6], C2 [×8], C3, C4 [×4], C22 [×11], C22 [×28], C5, S3 [×4], C6, C6 [×6], C6 [×4], C2×C4 [×6], D4 [×16], C23, C23 [×6], C23 [×14], D5 [×4], C10, C10 [×6], C10 [×4], Dic3 [×4], D6 [×16], C2×C6 [×11], C2×C6 [×12], C15, C22×C4, C2×D4 [×12], C24, C24, Dic5 [×4], D10 [×16], C2×C10 [×11], C2×C10 [×12], C2×Dic3 [×6], C3⋊D4 [×16], C22×S3 [×10], C22×C6, C22×C6 [×6], C22×C6 [×4], D15 [×4], C30, C30 [×6], C30 [×4], C22×D4, C2×Dic5 [×6], C5⋊D4 [×16], C22×D5 [×10], C22×C10, C22×C10 [×6], C22×C10 [×4], C22×Dic3, C2×C3⋊D4 [×12], S3×C23, C23×C6, Dic15 [×4], D30 [×4], D30 [×12], C2×C30 [×11], C2×C30 [×12], C22×Dic5, C2×C5⋊D4 [×12], C23×D5, C23×C10, C22×C3⋊D4, C2×Dic15 [×6], C157D4 [×16], C22×D15 [×6], C22×D15 [×4], C22×C30, C22×C30 [×6], C22×C30 [×4], C22×C5⋊D4, C22×Dic15, C2×C157D4 [×12], C23×D15, C23×C30, C22×C157D4
Quotients: C1, C2 [×15], C22 [×35], S3, D4 [×4], C23 [×15], D5, D6 [×7], C2×D4 [×6], C24, D10 [×7], C3⋊D4 [×4], C22×S3 [×7], D15, C22×D4, C5⋊D4 [×4], C22×D5 [×7], C2×C3⋊D4 [×6], S3×C23, D30 [×7], C2×C5⋊D4 [×6], C23×D5, C22×C3⋊D4, C157D4 [×4], C22×D15 [×7], C22×C5⋊D4, C2×C157D4 [×6], C23×D15, C22×C157D4

Smallest permutation representation of C22×C157D4
On 240 points
Generators in S240
(1 142)(2 143)(3 144)(4 145)(5 146)(6 147)(7 148)(8 149)(9 150)(10 136)(11 137)(12 138)(13 139)(14 140)(15 141)(16 130)(17 131)(18 132)(19 133)(20 134)(21 135)(22 121)(23 122)(24 123)(25 124)(26 125)(27 126)(28 127)(29 128)(30 129)(31 168)(32 169)(33 170)(34 171)(35 172)(36 173)(37 174)(38 175)(39 176)(40 177)(41 178)(42 179)(43 180)(44 166)(45 167)(46 152)(47 153)(48 154)(49 155)(50 156)(51 157)(52 158)(53 159)(54 160)(55 161)(56 162)(57 163)(58 164)(59 165)(60 151)(61 204)(62 205)(63 206)(64 207)(65 208)(66 209)(67 210)(68 196)(69 197)(70 198)(71 199)(72 200)(73 201)(74 202)(75 203)(76 182)(77 183)(78 184)(79 185)(80 186)(81 187)(82 188)(83 189)(84 190)(85 191)(86 192)(87 193)(88 194)(89 195)(90 181)(91 233)(92 234)(93 235)(94 236)(95 237)(96 238)(97 239)(98 240)(99 226)(100 227)(101 228)(102 229)(103 230)(104 231)(105 232)(106 225)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)(113 217)(114 218)(115 219)(116 220)(117 221)(118 222)(119 223)(120 224)
(1 80)(2 81)(3 82)(4 83)(5 84)(6 85)(7 86)(8 87)(9 88)(10 89)(11 90)(12 76)(13 77)(14 78)(15 79)(16 74)(17 75)(18 61)(19 62)(20 63)(21 64)(22 65)(23 66)(24 67)(25 68)(26 69)(27 70)(28 71)(29 72)(30 73)(31 107)(32 108)(33 109)(34 110)(35 111)(36 112)(37 113)(38 114)(39 115)(40 116)(41 117)(42 118)(43 119)(44 120)(45 106)(46 105)(47 91)(48 92)(49 93)(50 94)(51 95)(52 96)(53 97)(54 98)(55 99)(56 100)(57 101)(58 102)(59 103)(60 104)(121 208)(122 209)(123 210)(124 196)(125 197)(126 198)(127 199)(128 200)(129 201)(130 202)(131 203)(132 204)(133 205)(134 206)(135 207)(136 195)(137 181)(138 182)(139 183)(140 184)(141 185)(142 186)(143 187)(144 188)(145 189)(146 190)(147 191)(148 192)(149 193)(150 194)(151 231)(152 232)(153 233)(154 234)(155 235)(156 236)(157 237)(158 238)(159 239)(160 240)(161 226)(162 227)(163 228)(164 229)(165 230)(166 224)(167 225)(168 211)(169 212)(170 213)(171 214)(172 215)(173 216)(174 217)(175 218)(176 219)(177 220)(178 221)(179 222)(180 223)
(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)
(1 162 17 176)(2 161 18 175)(3 160 19 174)(4 159 20 173)(5 158 21 172)(6 157 22 171)(7 156 23 170)(8 155 24 169)(9 154 25 168)(10 153 26 167)(11 152 27 166)(12 151 28 180)(13 165 29 179)(14 164 30 178)(15 163 16 177)(31 150 48 124)(32 149 49 123)(33 148 50 122)(34 147 51 121)(35 146 52 135)(36 145 53 134)(37 144 54 133)(38 143 55 132)(39 142 56 131)(40 141 57 130)(41 140 58 129)(42 139 59 128)(43 138 60 127)(44 137 46 126)(45 136 47 125)(61 218 81 226)(62 217 82 240)(63 216 83 239)(64 215 84 238)(65 214 85 237)(66 213 86 236)(67 212 87 235)(68 211 88 234)(69 225 89 233)(70 224 90 232)(71 223 76 231)(72 222 77 230)(73 221 78 229)(74 220 79 228)(75 219 80 227)(91 197 106 195)(92 196 107 194)(93 210 108 193)(94 209 109 192)(95 208 110 191)(96 207 111 190)(97 206 112 189)(98 205 113 188)(99 204 114 187)(100 203 115 186)(101 202 116 185)(102 201 117 184)(103 200 118 183)(104 199 119 182)(105 198 120 181)
(1 75)(2 74)(3 73)(4 72)(5 71)(6 70)(7 69)(8 68)(9 67)(10 66)(11 65)(12 64)(13 63)(14 62)(15 61)(16 81)(17 80)(18 79)(19 78)(20 77)(21 76)(22 90)(23 89)(24 88)(25 87)(26 86)(27 85)(28 84)(29 83)(30 82)(31 108)(32 107)(33 106)(34 120)(35 119)(36 118)(37 117)(38 116)(39 115)(40 114)(41 113)(42 112)(43 111)(44 110)(45 109)(46 95)(47 94)(48 93)(49 92)(50 91)(51 105)(52 104)(53 103)(54 102)(55 101)(56 100)(57 99)(58 98)(59 97)(60 96)(121 181)(122 195)(123 194)(124 193)(125 192)(126 191)(127 190)(128 189)(129 188)(130 187)(131 186)(132 185)(133 184)(134 183)(135 182)(136 209)(137 208)(138 207)(139 206)(140 205)(141 204)(142 203)(143 202)(144 201)(145 200)(146 199)(147 198)(148 197)(149 196)(150 210)(151 238)(152 237)(153 236)(154 235)(155 234)(156 233)(157 232)(158 231)(159 230)(160 229)(161 228)(162 227)(163 226)(164 240)(165 239)(166 214)(167 213)(168 212)(169 211)(170 225)(171 224)(172 223)(173 222)(174 221)(175 220)(176 219)(177 218)(178 217)(179 216)(180 215)

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

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

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

132 conjugacy classes

class 1 2A···2G2H2I2J2K2L2M2N2O 3 4A4B4C4D5A5B6A···6O10A···10AD15A15B15C15D30A···30BH
order12···22222222234444556···610···101515151530···30
size11···1222230303030230303030222···22···222222···2

132 irreducible representations

dim111112222222222
type++++++++++++
imageC1C2C2C2C2S3D4D5D6D10C3⋊D4D15C5⋊D4D30C157D4
kernelC22×C157D4C22×Dic15C2×C157D4C23×D15C23×C30C23×C10C2×C30C23×C6C22×C10C22×C6C2×C10C24C2×C6C23C22
# reps11121114271484162832

Matrix representation of C22×C157D4 in GL6(𝔽61)

6000000
0600000
0060000
0006000
0000600
0000060
,
6000000
0600000
001000
000100
0000600
0000060
,
5380000
23530000
00606000
001000
00004547
00002223
,
6000000
1810000
001000
00606000
0000814
00005253
,
6000000
1810000
001000
00606000
0000431
00004318

G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,60],[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],[5,23,0,0,0,0,38,53,0,0,0,0,0,0,60,1,0,0,0,0,60,0,0,0,0,0,0,0,45,22,0,0,0,0,47,23],[60,18,0,0,0,0,0,1,0,0,0,0,0,0,1,60,0,0,0,0,0,60,0,0,0,0,0,0,8,52,0,0,0,0,14,53],[60,18,0,0,0,0,0,1,0,0,0,0,0,0,1,60,0,0,0,0,0,60,0,0,0,0,0,0,43,43,0,0,0,0,1,18] >;

C22×C157D4 in GAP, Magma, Sage, TeX

C_2^2\times C_{15}\rtimes_7D_4
% in TeX

G:=Group("C2^2xC15:7D4");
// GroupNames label

G:=SmallGroup(480,1179);
// by ID

G=gap.SmallGroup(480,1179);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,675,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^15=d^4=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=e*c*e=c^-1,e*d*e=d^-1>;
// generators/relations

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