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G = C2×C15⋊Q8order 240 = 24·3·5

Direct product of C2 and C15⋊Q8

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

Aliases: C2×C15⋊Q8, C30⋊Q8, C101Dic6, C61Dic10, C30.24C23, Dic5.14D6, Dic3.9D10, Dic15.15C22, C154(C2×Q8), C52(C2×Dic6), C32(C2×Dic10), (C2×C6).19D10, (C2×C10).19D6, (C6×Dic5).5C2, (C2×Dic5).4S3, (C2×Dic3).4D5, C22.17(S3×D5), C6.24(C22×D5), C10.24(C22×S3), (C2×C30).18C22, (C2×Dic15).8C2, (C10×Dic3).5C2, (C3×Dic5).16C22, (C5×Dic3).12C22, C2.24(C2×S3×D5), SmallGroup(240,148)

Series: Derived Chief Lower central Upper central

C1C30 — C2×C15⋊Q8
C1C5C15C30C3×Dic5C15⋊Q8 — C2×C15⋊Q8
C15C30 — C2×C15⋊Q8
C1C22

Generators and relations for C2×C15⋊Q8
 G = < a,b,c,d | a2=b15=c4=1, d2=c2, ab=ba, ac=ca, ad=da, cbc-1=b11, dbd-1=b4, dcd-1=c-1 >

Subgroups: 272 in 76 conjugacy classes, 40 normal (18 characteristic)
C1, C2, C2 [×2], C3, C4 [×6], C22, C5, C6, C6 [×2], C2×C4 [×3], Q8 [×4], C10, C10 [×2], Dic3 [×2], Dic3 [×2], C12 [×2], C2×C6, C15, C2×Q8, Dic5 [×2], Dic5 [×2], C20 [×2], C2×C10, Dic6 [×4], C2×Dic3, C2×Dic3, C2×C12, C30, C30 [×2], Dic10 [×4], C2×Dic5, C2×Dic5, C2×C20, C2×Dic6, C5×Dic3 [×2], C3×Dic5 [×2], Dic15 [×2], C2×C30, C2×Dic10, C15⋊Q8 [×4], C6×Dic5, C10×Dic3, C2×Dic15, C2×C15⋊Q8
Quotients: C1, C2 [×7], C22 [×7], S3, Q8 [×2], C23, D5, D6 [×3], C2×Q8, D10 [×3], Dic6 [×2], C22×S3, Dic10 [×2], C22×D5, C2×Dic6, S3×D5, C2×Dic10, C15⋊Q8 [×2], C2×S3×D5, C2×C15⋊Q8

Smallest permutation representation of C2×C15⋊Q8
Regular action on 240 points
Generators in S240
(1 43)(2 44)(3 45)(4 31)(5 32)(6 33)(7 34)(8 35)(9 36)(10 37)(11 38)(12 39)(13 40)(14 41)(15 42)(16 51)(17 52)(18 53)(19 54)(20 55)(21 56)(22 57)(23 58)(24 59)(25 60)(26 46)(27 47)(28 48)(29 49)(30 50)(61 95)(62 96)(63 97)(64 98)(65 99)(66 100)(67 101)(68 102)(69 103)(70 104)(71 105)(72 91)(73 92)(74 93)(75 94)(76 110)(77 111)(78 112)(79 113)(80 114)(81 115)(82 116)(83 117)(84 118)(85 119)(86 120)(87 106)(88 107)(89 108)(90 109)(121 163)(122 164)(123 165)(124 151)(125 152)(126 153)(127 154)(128 155)(129 156)(130 157)(131 158)(132 159)(133 160)(134 161)(135 162)(136 170)(137 171)(138 172)(139 173)(140 174)(141 175)(142 176)(143 177)(144 178)(145 179)(146 180)(147 166)(148 167)(149 168)(150 169)(181 215)(182 216)(183 217)(184 218)(185 219)(186 220)(187 221)(188 222)(189 223)(190 224)(191 225)(192 211)(193 212)(194 213)(195 214)(196 237)(197 238)(198 239)(199 240)(200 226)(201 227)(202 228)(203 229)(204 230)(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)
(1 119 16 104)(2 115 17 100)(3 111 18 96)(4 107 19 92)(5 118 20 103)(6 114 21 99)(7 110 22 95)(8 106 23 91)(9 117 24 102)(10 113 25 98)(11 109 26 94)(12 120 27 105)(13 116 28 101)(14 112 29 97)(15 108 30 93)(31 88 54 73)(32 84 55 69)(33 80 56 65)(34 76 57 61)(35 87 58 72)(36 83 59 68)(37 79 60 64)(38 90 46 75)(39 86 47 71)(40 82 48 67)(41 78 49 63)(42 89 50 74)(43 85 51 70)(44 81 52 66)(45 77 53 62)(121 224 139 239)(122 220 140 235)(123 216 141 231)(124 212 142 227)(125 223 143 238)(126 219 144 234)(127 215 145 230)(128 211 146 226)(129 222 147 237)(130 218 148 233)(131 214 149 229)(132 225 150 240)(133 221 136 236)(134 217 137 232)(135 213 138 228)(151 193 176 201)(152 189 177 197)(153 185 178 208)(154 181 179 204)(155 192 180 200)(156 188 166 196)(157 184 167 207)(158 195 168 203)(159 191 169 199)(160 187 170 210)(161 183 171 206)(162 194 172 202)(163 190 173 198)(164 186 174 209)(165 182 175 205)
(1 178 16 153)(2 167 17 157)(3 171 18 161)(4 175 19 165)(5 179 20 154)(6 168 21 158)(7 172 22 162)(8 176 23 151)(9 180 24 155)(10 169 25 159)(11 173 26 163)(12 177 27 152)(13 166 28 156)(14 170 29 160)(15 174 30 164)(31 141 54 123)(32 145 55 127)(33 149 56 131)(34 138 57 135)(35 142 58 124)(36 146 59 128)(37 150 60 132)(38 139 46 121)(39 143 47 125)(40 147 48 129)(41 136 49 133)(42 140 50 122)(43 144 51 126)(44 148 52 130)(45 137 53 134)(61 228 76 213)(62 232 77 217)(63 236 78 221)(64 240 79 225)(65 229 80 214)(66 233 81 218)(67 237 82 222)(68 226 83 211)(69 230 84 215)(70 234 85 219)(71 238 86 223)(72 227 87 212)(73 231 88 216)(74 235 89 220)(75 239 90 224)(91 201 106 193)(92 205 107 182)(93 209 108 186)(94 198 109 190)(95 202 110 194)(96 206 111 183)(97 210 112 187)(98 199 113 191)(99 203 114 195)(100 207 115 184)(101 196 116 188)(102 200 117 192)(103 204 118 181)(104 208 119 185)(105 197 120 189)

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

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

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

C2×C15⋊Q8 is a maximal subgroup of
Dic5.4D12  Dic55Dic6  Dic35Dic10  Dic155Q8  Dic151Q8  Dic3⋊Dic10  Dic15⋊Q8  D10⋊Dic6  Dic5.8D12  D6⋊Dic10  Dic3.D20  D308Q8  D62Dic10  D302Q8  D102Dic6  D304Q8  Dic15.D4  D64Dic10  Dic15.31D4  C60⋊Q8  C204Dic6  C20⋊Dic6  C23.D5⋊S3  Dic15.19D4  C6.(D4×D5)  (C2×C30)⋊Q8  (C2×C10)⋊8Dic6  Dic15.48D4  C2×D5×Dic6  C2×S3×Dic10  C15⋊2- 1+4
C2×C15⋊Q8 is a maximal quotient of
C60.6Q8  C12.Dic10  C20.Dic6  C60⋊Q8  C204Dic6  C20⋊Dic6  (C2×C30)⋊Q8  (C2×C10)⋊8Dic6  Dic15.48D4

42 conjugacy classes

class 1 2A2B2C 3 4A4B4C4D4E4F5A5B6A6B6C10A···10F12A12B12C12D15A15B20A···20H30A···30F
order122234444445566610···1012121212151520···2030···30
size111126610103030222222···210101010446···64···4

42 irreducible representations

dim11111222222222444
type++++++-+++++--+-+
imageC1C2C2C2C2S3Q8D5D6D6D10D10Dic6Dic10S3×D5C15⋊Q8C2×S3×D5
kernelC2×C15⋊Q8C15⋊Q8C6×Dic5C10×Dic3C2×Dic15C2×Dic5C30C2×Dic3Dic5C2×C10Dic3C2×C6C10C6C22C2C2
# reps14111122214248242

Matrix representation of C2×C15⋊Q8 in GL6(𝔽61)

6000000
0600000
001000
000100
0000600
0000060
,
100000
010000
00181800
00436000
0000060
0000160
,
21410000
16400000
0060000
0006000
00003734
00001024
,
7120000
6540000
00604300
000100
0000600
0000060

G:=sub<GL(6,GF(61))| [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],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,18,43,0,0,0,0,18,60,0,0,0,0,0,0,0,1,0,0,0,0,60,60],[21,16,0,0,0,0,41,40,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,37,10,0,0,0,0,34,24],[7,6,0,0,0,0,12,54,0,0,0,0,0,0,60,0,0,0,0,0,43,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60] >;

C2×C15⋊Q8 in GAP, Magma, Sage, TeX

C_2\times C_{15}\rtimes Q_8
% in TeX

G:=Group("C2xC15:Q8");
// GroupNames label

G:=SmallGroup(240,148);
// by ID

G=gap.SmallGroup(240,148);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-3,-5,48,121,55,490,6917]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^15=c^4=1,d^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^11,d*b*d^-1=b^4,d*c*d^-1=c^-1>;
// generators/relations

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