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G = Dic5.8D12order 480 = 25·3·5

4th non-split extension by Dic5 of D12 acting via D12/C12=C2

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: Dic5.8D12, D6⋊C41D5, C6.11(D4×D5), D6⋊Dic52C2, (C4×Dic5)⋊8S3, C30.31(C2×D4), C2.16(D5×D12), D304C43C2, C51(C427S3), C10.11(C2×D12), (C2×C20).179D6, C152(C4.4D4), D303C424C2, (C12×Dic5)⋊20C2, C6.17(C4○D20), (C2×C12).258D10, (C2×C30).40C23, (C2×Dic3).7D10, (C3×Dic5).50D4, (C22×S3).4D10, C10.20(C4○D12), C30.105(C4○D4), C6.38(D42D5), (C2×C60).381C22, (C2×Dic5).158D6, C31(Dic5.5D4), C2.12(Dic3.D10), C2.10(D6.D10), (C6×Dic5).179C22, (C2×Dic15).45C22, (C10×Dic3).24C22, (C22×D15).19C22, (C2×C15⋊Q8)⋊2C2, (C5×D6⋊C4)⋊24C2, (C2×C4).121(S3×D5), (C2×C5⋊D12).2C2, (S3×C2×C10).4C22, C22.129(C2×S3×D5), (C2×C6).52(C22×D5), (C2×C10).52(C22×S3), SmallGroup(480,426)

Series: Derived Chief Lower central Upper central

C1C2×C30 — Dic5.8D12
C1C5C15C30C2×C30C6×Dic5D6⋊Dic5 — Dic5.8D12
C15C2×C30 — Dic5.8D12
C1C22C2×C4

Generators and relations for Dic5.8D12
 G = < a,b,c,d | a10=c12=1, b2=d2=a5, bab-1=cac-1=dad-1=a-1, bc=cb, dbd-1=a5b, dcd-1=a5c-1 >

Subgroups: 908 in 152 conjugacy classes, 48 normal (44 characteristic)
C1, C2 [×3], C2 [×2], C3, C4 [×6], C22, C22 [×6], C5, S3 [×2], C6 [×3], C2×C4, C2×C4 [×4], D4 [×2], Q8 [×2], C23 [×2], D5, C10 [×3], C10, Dic3 [×2], C12 [×4], D6 [×6], C2×C6, C15, C42, C22⋊C4 [×4], C2×D4, C2×Q8, Dic5 [×2], Dic5 [×2], C20 [×2], D10 [×3], C2×C10, C2×C10 [×3], Dic6 [×2], D12 [×2], C2×Dic3, C2×Dic3, C2×C12, C2×C12 [×2], C22×S3, C22×S3, C5×S3, D15, C30 [×3], C4.4D4, Dic10 [×2], C2×Dic5 [×2], C2×Dic5, C5⋊D4 [×2], C2×C20, C2×C20, C22×D5, C22×C10, D6⋊C4, D6⋊C4 [×3], C4×C12, C2×Dic6, C2×D12, C5×Dic3, C3×Dic5 [×2], C3×Dic5, Dic15, C60, S3×C10 [×3], D30 [×3], C2×C30, C4×Dic5, D10⋊C4 [×2], C23.D5, C5×C22⋊C4, C2×Dic10, C2×C5⋊D4, C427S3, C5⋊D12 [×2], C15⋊Q8 [×2], C6×Dic5 [×2], C10×Dic3, C2×Dic15, C2×C60, S3×C2×C10, C22×D15, Dic5.5D4, D6⋊Dic5, D304C4, C12×Dic5, C5×D6⋊C4, D303C4, C2×C5⋊D12, C2×C15⋊Q8, Dic5.8D12
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], D12 [×2], C22×S3, C4.4D4, C22×D5, C2×D12, C4○D12 [×2], S3×D5, C4○D20, D4×D5, D42D5, C427S3, C2×S3×D5, Dic5.5D4, D6.D10, D5×D12, Dic3.D10, Dic5.8D12

Smallest permutation representation of Dic5.8D12
On 240 points
Generators in S240
(1 79 139 37 125 236 150 173 215 93)(2 94 216 174 151 237 126 38 140 80)(3 81 141 39 127 238 152 175 205 95)(4 96 206 176 153 239 128 40 142 82)(5 83 143 41 129 240 154 177 207 85)(6 86 208 178 155 229 130 42 144 84)(7 73 133 43 131 230 156 179 209 87)(8 88 210 180 145 231 132 44 134 74)(9 75 135 45 121 232 146 169 211 89)(10 90 212 170 147 233 122 46 136 76)(11 77 137 47 123 234 148 171 213 91)(12 92 214 172 149 235 124 48 138 78)(13 52 190 115 33 66 222 98 194 163)(14 164 195 99 223 67 34 116 191 53)(15 54 192 117 35 68 224 100 196 165)(16 166 197 101 225 69 36 118 181 55)(17 56 182 119 25 70 226 102 198 167)(18 168 199 103 227 71 26 120 183 57)(19 58 184 109 27 72 228 104 200 157)(20 158 201 105 217 61 28 110 185 59)(21 60 186 111 29 62 218 106 202 159)(22 160 203 107 219 63 30 112 187 49)(23 50 188 113 31 64 220 108 204 161)(24 162 193 97 221 65 32 114 189 51)
(1 108 236 188)(2 97 237 189)(3 98 238 190)(4 99 239 191)(5 100 240 192)(6 101 229 181)(7 102 230 182)(8 103 231 183)(9 104 232 184)(10 105 233 185)(11 106 234 186)(12 107 235 187)(13 141 66 175)(14 142 67 176)(15 143 68 177)(16 144 69 178)(17 133 70 179)(18 134 71 180)(19 135 72 169)(20 136 61 170)(21 137 62 171)(22 138 63 172)(23 139 64 173)(24 140 65 174)(25 209 167 43)(26 210 168 44)(27 211 157 45)(28 212 158 46)(29 213 159 47)(30 214 160 48)(31 215 161 37)(32 216 162 38)(33 205 163 39)(34 206 164 40)(35 207 165 41)(36 208 166 42)(49 78 219 149)(50 79 220 150)(51 80 221 151)(52 81 222 152)(53 82 223 153)(54 83 224 154)(55 84 225 155)(56 73 226 156)(57 74 227 145)(58 75 228 146)(59 76 217 147)(60 77 218 148)(85 196 129 117)(86 197 130 118)(87 198 131 119)(88 199 132 120)(89 200 121 109)(90 201 122 110)(91 202 123 111)(92 203 124 112)(93 204 125 113)(94 193 126 114)(95 194 127 115)(96 195 128 116)
(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)
(1 181 236 101)(2 100 237 192)(3 191 238 99)(4 98 239 190)(5 189 240 97)(6 108 229 188)(7 187 230 107)(8 106 231 186)(9 185 232 105)(10 104 233 184)(11 183 234 103)(12 102 235 182)(13 206 66 40)(14 39 67 205)(15 216 68 38)(16 37 69 215)(17 214 70 48)(18 47 71 213)(19 212 72 46)(20 45 61 211)(21 210 62 44)(22 43 63 209)(23 208 64 42)(24 41 65 207)(25 138 167 172)(26 171 168 137)(27 136 157 170)(28 169 158 135)(29 134 159 180)(30 179 160 133)(31 144 161 178)(32 177 162 143)(33 142 163 176)(34 175 164 141)(35 140 165 174)(36 173 166 139)(49 131 219 87)(50 86 220 130)(51 129 221 85)(52 96 222 128)(53 127 223 95)(54 94 224 126)(55 125 225 93)(56 92 226 124)(57 123 227 91)(58 90 228 122)(59 121 217 89)(60 88 218 132)(73 112 156 203)(74 202 145 111)(75 110 146 201)(76 200 147 109)(77 120 148 199)(78 198 149 119)(79 118 150 197)(80 196 151 117)(81 116 152 195)(82 194 153 115)(83 114 154 193)(84 204 155 113)

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

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

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

66 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D4E4F4G4H5A5B6A6B6C10A···10F10G10H10I10J12A12B12C12D12E···12L15A15B20A20B20C20D20E20F20G20H30A···30F60A···60H
order1222223444444445566610···10101010101212121212···121515202020202020202030···3060···60
size11111260222101010101260222222···212121212222210···10444444121212124···44···4

66 irreducible representations

dim111111112222222222224444444
type+++++++++++++++++++-++
imageC1C2C2C2C2C2C2C2S3D4D5D6D6C4○D4D10D10D10D12C4○D12C4○D20S3×D5D4×D5D42D5C2×S3×D5D6.D10D5×D12Dic3.D10
kernelDic5.8D12D6⋊Dic5D304C4C12×Dic5C5×D6⋊C4D303C4C2×C5⋊D12C2×C15⋊Q8C4×Dic5C3×Dic5D6⋊C4C2×Dic5C2×C20C30C2×Dic3C2×C12C22×S3Dic5C10C6C2×C4C6C6C22C2C2C2
# reps111111111222142224882222444

Matrix representation of Dic5.8D12 in GL6(𝔽61)

0600000
1440000
001000
000100
000010
000001
,
47160000
22140000
001000
000100
000010
000001
,
3270000
2290000
001100
0060000
00006053
0000461
,
5000000
57110000
001100
0006000
000018
0000060

G:=sub<GL(6,GF(61))| [0,1,0,0,0,0,60,44,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[47,22,0,0,0,0,16,14,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[32,2,0,0,0,0,7,29,0,0,0,0,0,0,1,60,0,0,0,0,1,0,0,0,0,0,0,0,60,46,0,0,0,0,53,1],[50,57,0,0,0,0,0,11,0,0,0,0,0,0,1,0,0,0,0,0,1,60,0,0,0,0,0,0,1,0,0,0,0,0,8,60] >;

Dic5.8D12 in GAP, Magma, Sage, TeX

{\rm Dic}_5._8D_{12}
% in TeX

G:=Group("Dic5.8D12");
// GroupNames label

G:=SmallGroup(480,426);
// by ID

G=gap.SmallGroup(480,426);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,141,219,58,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^10=c^12=1,b^2=d^2=a^5,b*a*b^-1=c*a*c^-1=d*a*d^-1=a^-1,b*c=c*b,d*b*d^-1=a^5*b,d*c*d^-1=a^5*c^-1>;
// generators/relations

׿
×
𝔽