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## G = C15×C8.C22order 480 = 25·3·5

### Direct product of C15 and C8.C22

direct product, metabelian, nilpotent (class 3), monomial, 2-elementary

Series: Derived Chief Lower central Upper central

 Derived series C1 — C4 — C15×C8.C22
 Chief series C1 — C2 — C4 — C20 — C60 — D4×C15 — C15×SD16 — C15×C8.C22
 Lower central C1 — C2 — C4 — C15×C8.C22
 Upper central C1 — C30 — C2×C60 — C15×C8.C22

Generators and relations for C15×C8.C22
G = < a,b,c,d | a15=b8=c2=d2=1, ab=ba, ac=ca, ad=da, cbc=b3, dbd=b5, dcd=b4c >

Subgroups: 168 in 120 conjugacy classes, 80 normal (48 characteristic)
C1, C2, C2 [×2], C3, C4 [×2], C4 [×3], C22, C22, C5, C6, C6 [×2], C8 [×2], C2×C4, C2×C4 [×2], D4, D4, Q8, Q8 [×2], Q8, C10, C10 [×2], C12 [×2], C12 [×3], C2×C6, C2×C6, C15, M4(2), SD16 [×2], Q16 [×2], C2×Q8, C4○D4, C20 [×2], C20 [×3], C2×C10, C2×C10, C24 [×2], C2×C12, C2×C12 [×2], C3×D4, C3×D4, C3×Q8, C3×Q8 [×2], C3×Q8, C30, C30 [×2], C8.C22, C40 [×2], C2×C20, C2×C20 [×2], C5×D4, C5×D4, C5×Q8, C5×Q8 [×2], C5×Q8, C3×M4(2), C3×SD16 [×2], C3×Q16 [×2], C6×Q8, C3×C4○D4, C60 [×2], C60 [×3], C2×C30, C2×C30, C5×M4(2), C5×SD16 [×2], C5×Q16 [×2], Q8×C10, C5×C4○D4, C3×C8.C22, C120 [×2], C2×C60, C2×C60 [×2], D4×C15, D4×C15, Q8×C15, Q8×C15 [×2], Q8×C15, C5×C8.C22, C15×M4(2), C15×SD16 [×2], C15×Q16 [×2], Q8×C30, C15×C4○D4, C15×C8.C22
Quotients: C1, C2 [×7], C3, C22 [×7], C5, C6 [×7], D4 [×2], C23, C10 [×7], C2×C6 [×7], C15, C2×D4, C2×C10 [×7], C3×D4 [×2], C22×C6, C30 [×7], C8.C22, C5×D4 [×2], C22×C10, C6×D4, C2×C30 [×7], D4×C10, C3×C8.C22, D4×C15 [×2], C22×C30, C5×C8.C22, D4×C30, C15×C8.C22

Smallest permutation representation of C15×C8.C22
On 240 points
Generators in S240
(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)
(1 237 187 28 107 198 43 72)(2 238 188 29 108 199 44 73)(3 239 189 30 109 200 45 74)(4 240 190 16 110 201 31 75)(5 226 191 17 111 202 32 61)(6 227 192 18 112 203 33 62)(7 228 193 19 113 204 34 63)(8 229 194 20 114 205 35 64)(9 230 195 21 115 206 36 65)(10 231 181 22 116 207 37 66)(11 232 182 23 117 208 38 67)(12 233 183 24 118 209 39 68)(13 234 184 25 119 210 40 69)(14 235 185 26 120 196 41 70)(15 236 186 27 106 197 42 71)(46 172 152 130 222 138 94 90)(47 173 153 131 223 139 95 76)(48 174 154 132 224 140 96 77)(49 175 155 133 225 141 97 78)(50 176 156 134 211 142 98 79)(51 177 157 135 212 143 99 80)(52 178 158 121 213 144 100 81)(53 179 159 122 214 145 101 82)(54 180 160 123 215 146 102 83)(55 166 161 124 216 147 103 84)(56 167 162 125 217 148 104 85)(57 168 163 126 218 149 105 86)(58 169 164 127 219 150 91 87)(59 170 165 128 220 136 92 88)(60 171 151 129 221 137 93 89)
(1 172)(2 173)(3 174)(4 175)(5 176)(6 177)(7 178)(8 179)(9 180)(10 166)(11 167)(12 168)(13 169)(14 170)(15 171)(16 155)(17 156)(18 157)(19 158)(20 159)(21 160)(22 161)(23 162)(24 163)(25 164)(26 165)(27 151)(28 152)(29 153)(30 154)(31 133)(32 134)(33 135)(34 121)(35 122)(36 123)(37 124)(38 125)(39 126)(40 127)(41 128)(42 129)(43 130)(44 131)(45 132)(46 198)(47 199)(48 200)(49 201)(50 202)(51 203)(52 204)(53 205)(54 206)(55 207)(56 208)(57 209)(58 210)(59 196)(60 197)(61 98)(62 99)(63 100)(64 101)(65 102)(66 103)(67 104)(68 105)(69 91)(70 92)(71 93)(72 94)(73 95)(74 96)(75 97)(76 188)(77 189)(78 190)(79 191)(80 192)(81 193)(82 194)(83 195)(84 181)(85 182)(86 183)(87 184)(88 185)(89 186)(90 187)(106 137)(107 138)(108 139)(109 140)(110 141)(111 142)(112 143)(113 144)(114 145)(115 146)(116 147)(117 148)(118 149)(119 150)(120 136)(211 226)(212 227)(213 228)(214 229)(215 230)(216 231)(217 232)(218 233)(219 234)(220 235)(221 236)(222 237)(223 238)(224 239)(225 240)
(16 75)(17 61)(18 62)(19 63)(20 64)(21 65)(22 66)(23 67)(24 68)(25 69)(26 70)(27 71)(28 72)(29 73)(30 74)(76 131)(77 132)(78 133)(79 134)(80 135)(81 121)(82 122)(83 123)(84 124)(85 125)(86 126)(87 127)(88 128)(89 129)(90 130)(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)(196 235)(197 236)(198 237)(199 238)(200 239)(201 240)(202 226)(203 227)(204 228)(205 229)(206 230)(207 231)(208 232)(209 233)(210 234)

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

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

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

165 conjugacy classes

 class 1 2A 2B 2C 3A 3B 4A 4B 4C 4D 4E 5A 5B 5C 5D 6A 6B 6C 6D 6E 6F 8A 8B 10A 10B 10C 10D 10E 10F 10G 10H 10I 10J 10K 10L 12A 12B 12C 12D 12E ··· 12J 15A ··· 15H 20A ··· 20H 20I ··· 20T 24A 24B 24C 24D 30A ··· 30H 30I ··· 30P 30Q ··· 30X 40A ··· 40H 60A ··· 60P 60Q ··· 60AN 120A ··· 120P order 1 2 2 2 3 3 4 4 4 4 4 5 5 5 5 6 6 6 6 6 6 8 8 10 10 10 10 10 10 10 10 10 10 10 10 12 12 12 12 12 ··· 12 15 ··· 15 20 ··· 20 20 ··· 20 24 24 24 24 30 ··· 30 30 ··· 30 30 ··· 30 40 ··· 40 60 ··· 60 60 ··· 60 120 ··· 120 size 1 1 2 4 1 1 2 2 4 4 4 1 1 1 1 1 1 2 2 4 4 4 4 1 1 1 1 2 2 2 2 4 4 4 4 2 2 2 2 4 ··· 4 1 ··· 1 2 ··· 2 4 ··· 4 4 4 4 4 1 ··· 1 2 ··· 2 4 ··· 4 4 ··· 4 2 ··· 2 4 ··· 4 4 ··· 4

165 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 4 type + + + + + + + + - image C1 C2 C2 C2 C2 C2 C3 C5 C6 C6 C6 C6 C6 C10 C10 C10 C10 C10 C15 C30 C30 C30 C30 C30 D4 D4 C3×D4 C3×D4 C5×D4 C5×D4 D4×C15 D4×C15 C8.C22 C3×C8.C22 C5×C8.C22 C15×C8.C22 kernel C15×C8.C22 C15×M4(2) C15×SD16 C15×Q16 Q8×C30 C15×C4○D4 C5×C8.C22 C3×C8.C22 C5×M4(2) C5×SD16 C5×Q16 Q8×C10 C5×C4○D4 C3×M4(2) C3×SD16 C3×Q16 C6×Q8 C3×C4○D4 C8.C22 M4(2) SD16 Q16 C2×Q8 C4○D4 C60 C2×C30 C20 C2×C10 C12 C2×C6 C4 C22 C15 C5 C3 C1 # reps 1 1 2 2 1 1 2 4 2 4 4 2 2 4 8 8 4 4 8 8 16 16 8 8 1 1 2 2 4 4 8 8 1 2 4 8

Matrix representation of C15×C8.C22 in GL6(𝔽241)

 225 0 0 0 0 0 0 225 0 0 0 0 0 0 205 0 0 0 0 0 0 205 0 0 0 0 0 0 205 0 0 0 0 0 0 205
,
 184 57 0 0 0 0 36 57 0 0 0 0 0 0 158 2 85 0 0 0 0 0 239 85 0 0 4 87 239 239 0 0 71 158 85 85
,
 184 57 0 0 0 0 91 57 0 0 0 0 0 0 240 0 0 0 0 0 0 0 0 1 0 0 239 240 1 1 0 0 0 1 0 0
,
 240 0 0 0 0 0 0 240 0 0 0 0 0 0 1 0 240 240 0 0 0 1 0 0 0 0 0 0 240 0 0 0 0 0 0 240

G:=sub<GL(6,GF(241))| [225,0,0,0,0,0,0,225,0,0,0,0,0,0,205,0,0,0,0,0,0,205,0,0,0,0,0,0,205,0,0,0,0,0,0,205],[184,36,0,0,0,0,57,57,0,0,0,0,0,0,158,0,4,71,0,0,2,0,87,158,0,0,85,239,239,85,0,0,0,85,239,85],[184,91,0,0,0,0,57,57,0,0,0,0,0,0,240,0,239,0,0,0,0,0,240,1,0,0,0,0,1,0,0,0,0,1,1,0],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,240,0,240,0,0,0,240,0,0,240] >;

C15×C8.C22 in GAP, Magma, Sage, TeX

C_{15}\times C_8.C_2^2
% in TeX

G:=Group("C15xC8.C2^2");
// GroupNames label

G:=SmallGroup(480,942);
// by ID

G=gap.SmallGroup(480,942);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-5,-2,-2,1709,1688,5126,15125,7572,124]);
// Polycyclic

G:=Group<a,b,c,d|a^15=b^8=c^2=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^3,d*b*d=b^5,d*c*d=b^4*c>;
// generators/relations

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