direct product, metabelian, supersoluble, monomial, A-group
Aliases: C22×C3⋊D15, C30⋊6D6, C6⋊2D30, C62⋊5D5, (C2×C30)⋊7S3, (C6×C30)⋊3C2, (C3×C6)⋊6D10, (C2×C6)⋊5D15, (C3×C15)⋊7C23, C15⋊7(C22×S3), (C3×C30)⋊6C22, C3⋊2(C22×D15), C32⋊7(C22×D5), C10⋊2(C2×C3⋊S3), C5⋊2(C22×C3⋊S3), (C2×C10)⋊5(C3⋊S3), SmallGroup(360,161)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C15 — C22×C3⋊D15 |
Generators and relations for C22×C3⋊D15
G = < a,b,c,d,e | a2=b2=c3=d15=e2=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece=c-1, ede=d-1 >
Subgroups: 1512 in 192 conjugacy classes, 71 normal (9 characteristic)
C1, C2, C2, C3, C22, C22, C5, S3, C6, C23, C32, D5, C10, D6, C2×C6, C15, C3⋊S3, C3×C6, D10, C2×C10, C22×S3, D15, C30, C2×C3⋊S3, C62, C22×D5, C3×C15, D30, C2×C30, C22×C3⋊S3, C3⋊D15, C3×C30, C22×D15, C2×C3⋊D15, C6×C30, C22×C3⋊D15
Quotients: C1, C2, C22, S3, C23, D5, D6, C3⋊S3, D10, C22×S3, D15, C2×C3⋊S3, C22×D5, D30, C22×C3⋊S3, C3⋊D15, C22×D15, C2×C3⋊D15, C22×C3⋊D15
►On 180 points
Generators in S180
(1 102)(2 103)(3 104)(4 105)(5 91)(6 92)(7 93)(8 94)(9 95)(10 96)(11 97)(12 98)(13 99)(14 100)(15 101)(16 108)(17 109)(18 110)(19 111)(20 112)(21 113)(22 114)(23 115)(24 116)(25 117)(26 118)(27 119)(28 120)(29 106)(30 107)(31 121)(32 122)(33 123)(34 124)(35 125)(36 126)(37 127)(38 128)(39 129)(40 130)(41 131)(42 132)(43 133)(44 134)(45 135)(46 138)(47 139)(48 140)(49 141)(50 142)(51 143)(52 144)(53 145)(54 146)(55 147)(56 148)(57 149)(58 150)(59 136)(60 137)(61 151)(62 152)(63 153)(64 154)(65 155)(66 156)(67 157)(68 158)(69 159)(70 160)(71 161)(72 162)(73 163)(74 164)(75 165)(76 166)(77 167)(78 168)(79 169)(80 170)(81 171)(82 172)(83 173)(84 174)(85 175)(86 176)(87 177)(88 178)(89 179)(90 180)
(1 55)(2 56)(3 57)(4 58)(5 59)(6 60)(7 46)(8 47)(9 48)(10 49)(11 50)(12 51)(13 52)(14 53)(15 54)(16 72)(17 73)(18 74)(19 75)(20 61)(21 62)(22 63)(23 64)(24 65)(25 66)(26 67)(27 68)(28 69)(29 70)(30 71)(31 80)(32 81)(33 82)(34 83)(35 84)(36 85)(37 86)(38 87)(39 88)(40 89)(41 90)(42 76)(43 77)(44 78)(45 79)(91 136)(92 137)(93 138)(94 139)(95 140)(96 141)(97 142)(98 143)(99 144)(100 145)(101 146)(102 147)(103 148)(104 149)(105 150)(106 160)(107 161)(108 162)(109 163)(110 164)(111 165)(112 151)(113 152)(114 153)(115 154)(116 155)(117 156)(118 157)(119 158)(120 159)(121 170)(122 171)(123 172)(124 173)(125 174)(126 175)(127 176)(128 177)(129 178)(130 179)(131 180)(132 166)(133 167)(134 168)(135 169)
(1 35 19)(2 36 20)(3 37 21)(4 38 22)(5 39 23)(6 40 24)(7 41 25)(8 42 26)(9 43 27)(10 44 28)(11 45 29)(12 31 30)(13 32 16)(14 33 17)(15 34 18)(46 90 66)(47 76 67)(48 77 68)(49 78 69)(50 79 70)(51 80 71)(52 81 72)(53 82 73)(54 83 74)(55 84 75)(56 85 61)(57 86 62)(58 87 63)(59 88 64)(60 89 65)(91 129 115)(92 130 116)(93 131 117)(94 132 118)(95 133 119)(96 134 120)(97 135 106)(98 121 107)(99 122 108)(100 123 109)(101 124 110)(102 125 111)(103 126 112)(104 127 113)(105 128 114)(136 178 154)(137 179 155)(138 180 156)(139 166 157)(140 167 158)(141 168 159)(142 169 160)(143 170 161)(144 171 162)(145 172 163)(146 173 164)(147 174 165)(148 175 151)(149 176 152)(150 177 153)
(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)
(1 15)(2 14)(3 13)(4 12)(5 11)(6 10)(7 9)(16 37)(17 36)(18 35)(19 34)(20 33)(21 32)(22 31)(23 45)(24 44)(25 43)(26 42)(27 41)(28 40)(29 39)(30 38)(46 48)(49 60)(50 59)(51 58)(52 57)(53 56)(54 55)(61 82)(62 81)(63 80)(64 79)(65 78)(66 77)(67 76)(68 90)(69 89)(70 88)(71 87)(72 86)(73 85)(74 84)(75 83)(91 97)(92 96)(93 95)(98 105)(99 104)(100 103)(101 102)(106 129)(107 128)(108 127)(109 126)(110 125)(111 124)(112 123)(113 122)(114 121)(115 135)(116 134)(117 133)(118 132)(119 131)(120 130)(136 142)(137 141)(138 140)(143 150)(144 149)(145 148)(146 147)(151 172)(152 171)(153 170)(154 169)(155 168)(156 167)(157 166)(158 180)(159 179)(160 178)(161 177)(162 176)(163 175)(164 174)(165 173)
G:=sub<Sym(180)| (1,102)(2,103)(3,104)(4,105)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,101)(16,108)(17,109)(18,110)(19,111)(20,112)(21,113)(22,114)(23,115)(24,116)(25,117)(26,118)(27,119)(28,120)(29,106)(30,107)(31,121)(32,122)(33,123)(34,124)(35,125)(36,126)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,133)(44,134)(45,135)(46,138)(47,139)(48,140)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,149)(58,150)(59,136)(60,137)(61,151)(62,152)(63,153)(64,154)(65,155)(66,156)(67,157)(68,158)(69,159)(70,160)(71,161)(72,162)(73,163)(74,164)(75,165)(76,166)(77,167)(78,168)(79,169)(80,170)(81,171)(82,172)(83,173)(84,174)(85,175)(86,176)(87,177)(88,178)(89,179)(90,180), (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,46)(8,47)(9,48)(10,49)(11,50)(12,51)(13,52)(14,53)(15,54)(16,72)(17,73)(18,74)(19,75)(20,61)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,70)(30,71)(31,80)(32,81)(33,82)(34,83)(35,84)(36,85)(37,86)(38,87)(39,88)(40,89)(41,90)(42,76)(43,77)(44,78)(45,79)(91,136)(92,137)(93,138)(94,139)(95,140)(96,141)(97,142)(98,143)(99,144)(100,145)(101,146)(102,147)(103,148)(104,149)(105,150)(106,160)(107,161)(108,162)(109,163)(110,164)(111,165)(112,151)(113,152)(114,153)(115,154)(116,155)(117,156)(118,157)(119,158)(120,159)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,166)(133,167)(134,168)(135,169), (1,35,19)(2,36,20)(3,37,21)(4,38,22)(5,39,23)(6,40,24)(7,41,25)(8,42,26)(9,43,27)(10,44,28)(11,45,29)(12,31,30)(13,32,16)(14,33,17)(15,34,18)(46,90,66)(47,76,67)(48,77,68)(49,78,69)(50,79,70)(51,80,71)(52,81,72)(53,82,73)(54,83,74)(55,84,75)(56,85,61)(57,86,62)(58,87,63)(59,88,64)(60,89,65)(91,129,115)(92,130,116)(93,131,117)(94,132,118)(95,133,119)(96,134,120)(97,135,106)(98,121,107)(99,122,108)(100,123,109)(101,124,110)(102,125,111)(103,126,112)(104,127,113)(105,128,114)(136,178,154)(137,179,155)(138,180,156)(139,166,157)(140,167,158)(141,168,159)(142,169,160)(143,170,161)(144,171,162)(145,172,163)(146,173,164)(147,174,165)(148,175,151)(149,176,152)(150,177,153), (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), (1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,45)(24,44)(25,43)(26,42)(27,41)(28,40)(29,39)(30,38)(46,48)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,90)(69,89)(70,88)(71,87)(72,86)(73,85)(74,84)(75,83)(91,97)(92,96)(93,95)(98,105)(99,104)(100,103)(101,102)(106,129)(107,128)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,135)(116,134)(117,133)(118,132)(119,131)(120,130)(136,142)(137,141)(138,140)(143,150)(144,149)(145,148)(146,147)(151,172)(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,180)(159,179)(160,178)(161,177)(162,176)(163,175)(164,174)(165,173)>;
G:=Group( (1,102)(2,103)(3,104)(4,105)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,101)(16,108)(17,109)(18,110)(19,111)(20,112)(21,113)(22,114)(23,115)(24,116)(25,117)(26,118)(27,119)(28,120)(29,106)(30,107)(31,121)(32,122)(33,123)(34,124)(35,125)(36,126)(37,127)(38,128)(39,129)(40,130)(41,131)(42,132)(43,133)(44,134)(45,135)(46,138)(47,139)(48,140)(49,141)(50,142)(51,143)(52,144)(53,145)(54,146)(55,147)(56,148)(57,149)(58,150)(59,136)(60,137)(61,151)(62,152)(63,153)(64,154)(65,155)(66,156)(67,157)(68,158)(69,159)(70,160)(71,161)(72,162)(73,163)(74,164)(75,165)(76,166)(77,167)(78,168)(79,169)(80,170)(81,171)(82,172)(83,173)(84,174)(85,175)(86,176)(87,177)(88,178)(89,179)(90,180), (1,55)(2,56)(3,57)(4,58)(5,59)(6,60)(7,46)(8,47)(9,48)(10,49)(11,50)(12,51)(13,52)(14,53)(15,54)(16,72)(17,73)(18,74)(19,75)(20,61)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,70)(30,71)(31,80)(32,81)(33,82)(34,83)(35,84)(36,85)(37,86)(38,87)(39,88)(40,89)(41,90)(42,76)(43,77)(44,78)(45,79)(91,136)(92,137)(93,138)(94,139)(95,140)(96,141)(97,142)(98,143)(99,144)(100,145)(101,146)(102,147)(103,148)(104,149)(105,150)(106,160)(107,161)(108,162)(109,163)(110,164)(111,165)(112,151)(113,152)(114,153)(115,154)(116,155)(117,156)(118,157)(119,158)(120,159)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,166)(133,167)(134,168)(135,169), (1,35,19)(2,36,20)(3,37,21)(4,38,22)(5,39,23)(6,40,24)(7,41,25)(8,42,26)(9,43,27)(10,44,28)(11,45,29)(12,31,30)(13,32,16)(14,33,17)(15,34,18)(46,90,66)(47,76,67)(48,77,68)(49,78,69)(50,79,70)(51,80,71)(52,81,72)(53,82,73)(54,83,74)(55,84,75)(56,85,61)(57,86,62)(58,87,63)(59,88,64)(60,89,65)(91,129,115)(92,130,116)(93,131,117)(94,132,118)(95,133,119)(96,134,120)(97,135,106)(98,121,107)(99,122,108)(100,123,109)(101,124,110)(102,125,111)(103,126,112)(104,127,113)(105,128,114)(136,178,154)(137,179,155)(138,180,156)(139,166,157)(140,167,158)(141,168,159)(142,169,160)(143,170,161)(144,171,162)(145,172,163)(146,173,164)(147,174,165)(148,175,151)(149,176,152)(150,177,153), (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), (1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,45)(24,44)(25,43)(26,42)(27,41)(28,40)(29,39)(30,38)(46,48)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,90)(69,89)(70,88)(71,87)(72,86)(73,85)(74,84)(75,83)(91,97)(92,96)(93,95)(98,105)(99,104)(100,103)(101,102)(106,129)(107,128)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,135)(116,134)(117,133)(118,132)(119,131)(120,130)(136,142)(137,141)(138,140)(143,150)(144,149)(145,148)(146,147)(151,172)(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,180)(159,179)(160,178)(161,177)(162,176)(163,175)(164,174)(165,173) );
G=PermutationGroup([[(1,102),(2,103),(3,104),(4,105),(5,91),(6,92),(7,93),(8,94),(9,95),(10,96),(11,97),(12,98),(13,99),(14,100),(15,101),(16,108),(17,109),(18,110),(19,111),(20,112),(21,113),(22,114),(23,115),(24,116),(25,117),(26,118),(27,119),(28,120),(29,106),(30,107),(31,121),(32,122),(33,123),(34,124),(35,125),(36,126),(37,127),(38,128),(39,129),(40,130),(41,131),(42,132),(43,133),(44,134),(45,135),(46,138),(47,139),(48,140),(49,141),(50,142),(51,143),(52,144),(53,145),(54,146),(55,147),(56,148),(57,149),(58,150),(59,136),(60,137),(61,151),(62,152),(63,153),(64,154),(65,155),(66,156),(67,157),(68,158),(69,159),(70,160),(71,161),(72,162),(73,163),(74,164),(75,165),(76,166),(77,167),(78,168),(79,169),(80,170),(81,171),(82,172),(83,173),(84,174),(85,175),(86,176),(87,177),(88,178),(89,179),(90,180)], [(1,55),(2,56),(3,57),(4,58),(5,59),(6,60),(7,46),(8,47),(9,48),(10,49),(11,50),(12,51),(13,52),(14,53),(15,54),(16,72),(17,73),(18,74),(19,75),(20,61),(21,62),(22,63),(23,64),(24,65),(25,66),(26,67),(27,68),(28,69),(29,70),(30,71),(31,80),(32,81),(33,82),(34,83),(35,84),(36,85),(37,86),(38,87),(39,88),(40,89),(41,90),(42,76),(43,77),(44,78),(45,79),(91,136),(92,137),(93,138),(94,139),(95,140),(96,141),(97,142),(98,143),(99,144),(100,145),(101,146),(102,147),(103,148),(104,149),(105,150),(106,160),(107,161),(108,162),(109,163),(110,164),(111,165),(112,151),(113,152),(114,153),(115,154),(116,155),(117,156),(118,157),(119,158),(120,159),(121,170),(122,171),(123,172),(124,173),(125,174),(126,175),(127,176),(128,177),(129,178),(130,179),(131,180),(132,166),(133,167),(134,168),(135,169)], [(1,35,19),(2,36,20),(3,37,21),(4,38,22),(5,39,23),(6,40,24),(7,41,25),(8,42,26),(9,43,27),(10,44,28),(11,45,29),(12,31,30),(13,32,16),(14,33,17),(15,34,18),(46,90,66),(47,76,67),(48,77,68),(49,78,69),(50,79,70),(51,80,71),(52,81,72),(53,82,73),(54,83,74),(55,84,75),(56,85,61),(57,86,62),(58,87,63),(59,88,64),(60,89,65),(91,129,115),(92,130,116),(93,131,117),(94,132,118),(95,133,119),(96,134,120),(97,135,106),(98,121,107),(99,122,108),(100,123,109),(101,124,110),(102,125,111),(103,126,112),(104,127,113),(105,128,114),(136,178,154),(137,179,155),(138,180,156),(139,166,157),(140,167,158),(141,168,159),(142,169,160),(143,170,161),(144,171,162),(145,172,163),(146,173,164),(147,174,165),(148,175,151),(149,176,152),(150,177,153)], [(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)], [(1,15),(2,14),(3,13),(4,12),(5,11),(6,10),(7,9),(16,37),(17,36),(18,35),(19,34),(20,33),(21,32),(22,31),(23,45),(24,44),(25,43),(26,42),(27,41),(28,40),(29,39),(30,38),(46,48),(49,60),(50,59),(51,58),(52,57),(53,56),(54,55),(61,82),(62,81),(63,80),(64,79),(65,78),(66,77),(67,76),(68,90),(69,89),(70,88),(71,87),(72,86),(73,85),(74,84),(75,83),(91,97),(92,96),(93,95),(98,105),(99,104),(100,103),(101,102),(106,129),(107,128),(108,127),(109,126),(110,125),(111,124),(112,123),(113,122),(114,121),(115,135),(116,134),(117,133),(118,132),(119,131),(120,130),(136,142),(137,141),(138,140),(143,150),(144,149),(145,148),(146,147),(151,172),(152,171),(153,170),(154,169),(155,168),(156,167),(157,166),(158,180),(159,179),(160,178),(161,177),(162,176),(163,175),(164,174),(165,173)]])
96 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 3A | 3B | 3C | 3D | 5A | 5B | 6A | ··· | 6L | 10A | ··· | 10F | 15A | ··· | 15P | 30A | ··· | 30AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 5 | 5 | 6 | ··· | 6 | 10 | ··· | 10 | 15 | ··· | 15 | 30 | ··· | 30 |
| size | 1 | 1 | 1 | 1 | 45 | 45 | 45 | 45 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
96 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + |
| image | C1 | C2 | C2 | S3 | D5 | D6 | D10 | D15 | D30 |
| kernel | C22×C3⋊D15 | C2×C3⋊D15 | C6×C30 | C2×C30 | C62 | C30 | C3×C6 | C2×C6 | C6 |
| # reps | 1 | 6 | 1 | 4 | 2 | 12 | 6 | 16 | 48 |
Matrix representation of C22×C3⋊D15 ►in GL4(𝔽31) generated by
| 30 | 0 | 0 | 0 |
| 0 | 30 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 30 | 0 |
| 0 | 0 | 0 | 30 |
| 16 | 5 | 0 | 0 |
| 26 | 14 | 0 | 0 |
| 0 | 0 | 19 | 3 |
| 0 | 0 | 28 | 11 |
| 23 | 20 | 0 | 0 |
| 11 | 15 | 0 | 0 |
| 0 | 0 | 13 | 13 |
| 0 | 0 | 18 | 30 |
| 12 | 12 | 0 | 0 |
| 1 | 19 | 0 | 0 |
| 0 | 0 | 13 | 13 |
| 0 | 0 | 30 | 18 |
G:=sub<GL(4,GF(31))| [30,0,0,0,0,30,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,30,0,0,0,0,30],[16,26,0,0,5,14,0,0,0,0,19,28,0,0,3,11],[23,11,0,0,20,15,0,0,0,0,13,18,0,0,13,30],[12,1,0,0,12,19,0,0,0,0,13,30,0,0,13,18] >;
C22×C3⋊D15 in GAP, Magma, Sage, TeX
C_2^2\times C_3\rtimes D_{15} % in TeX
G:=Group("C2^2xC3:D15"); // GroupNames label
G:=SmallGroup(360,161);
// by ID
G=gap.SmallGroup(360,161);
# by ID
G:=PCGroup([6,-2,-2,-2,-3,-3,-5,387,1444,10373]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^3=d^15=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,c*d=d*c,e*c*e=c^-1,e*d*e=d^-1>;
// generators/relations