metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D18.4D4, C23.9D18, C2.8(D4×D9), D18⋊C4⋊5C2, C4⋊Dic9⋊4C2, C22⋊C4⋊3D9, (C2×C12).3D6, C6.80(S3×D4), (C2×C4).26D18, C18.19(C2×D4), Dic9⋊C4⋊10C2, C18.8(C4○D4), (C2×C36).3C22, C3.(C23.9D6), (C22×C6).43D6, C6.78(C4○D12), C18.D4⋊4C2, C2.8(D4⋊2D9), (C2×C18).24C23, C9⋊1(C22.D4), C6.76(D4⋊2S3), C2.10(D36⋊5C2), (C2×Dic9).5C22, C22.42(C22×D9), (C22×C18).13C22, (C22×D9).17C22, (C2×C4×D9)⋊10C2, (C9×C22⋊C4)⋊5C2, (C2×C9⋊D4).3C2, (C3×C22⋊C4).7S3, (C2×C6).181(C22×S3), SmallGroup(288,93)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C23.9D18
G = < a,b,c,d,e | a2=b2=c2=1, d18=e2=b, ab=ba, dad-1=ac=ca, eae-1=abc, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d17 >
Subgroups: 524 in 117 conjugacy classes, 40 normal (38 characteristic)
C1, C2, C2, C3, C4, C22, C22, S3, C6, C6, C2×C4, C2×C4, D4, C23, C23, C9, Dic3, C12, D6, C2×C6, C2×C6, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, D9, C18, C18, C4×S3, C2×Dic3, C3⋊D4, C2×C12, C22×S3, C22×C6, C22.D4, Dic9, C36, D18, D18, C2×C18, C2×C18, Dic3⋊C4, C4⋊Dic3, D6⋊C4, C6.D4, C3×C22⋊C4, S3×C2×C4, C2×C3⋊D4, C4×D9, C2×Dic9, C9⋊D4, C2×C36, C22×D9, C22×C18, C23.9D6, Dic9⋊C4, C4⋊Dic9, D18⋊C4, C18.D4, C9×C22⋊C4, C2×C4×D9, C2×C9⋊D4, C23.9D18
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, D9, C22×S3, C22.D4, D18, C4○D12, S3×D4, D4⋊2S3, C22×D9, C23.9D6, D36⋊5C2, D4×D9, D4⋊2D9, C23.9D18
►On 144 points
Generators in S144
(1 138)(2 102)(3 140)(4 104)(5 142)(6 106)(7 144)(8 108)(9 110)(10 74)(11 112)(12 76)(13 114)(14 78)(15 116)(16 80)(17 118)(18 82)(19 120)(20 84)(21 122)(22 86)(23 124)(24 88)(25 126)(26 90)(27 128)(28 92)(29 130)(30 94)(31 132)(32 96)(33 134)(34 98)(35 136)(36 100)(37 103)(38 141)(39 105)(40 143)(41 107)(42 109)(43 73)(44 111)(45 75)(46 113)(47 77)(48 115)(49 79)(50 117)(51 81)(52 119)(53 83)(54 121)(55 85)(56 123)(57 87)(58 125)(59 89)(60 127)(61 91)(62 129)(63 93)(64 131)(65 95)(66 133)(67 97)(68 135)(69 99)(70 137)(71 101)(72 139)
(1 19)(2 20)(3 21)(4 22)(5 23)(6 24)(7 25)(8 26)(9 27)(10 28)(11 29)(12 30)(13 31)(14 32)(15 33)(16 34)(17 35)(18 36)(37 55)(38 56)(39 57)(40 58)(41 59)(42 60)(43 61)(44 62)(45 63)(46 64)(47 65)(48 66)(49 67)(50 68)(51 69)(52 70)(53 71)(54 72)(73 91)(74 92)(75 93)(76 94)(77 95)(78 96)(79 97)(80 98)(81 99)(82 100)(83 101)(84 102)(85 103)(86 104)(87 105)(88 106)(89 107)(90 108)(109 127)(110 128)(111 129)(112 130)(113 131)(114 132)(115 133)(116 134)(117 135)(118 136)(119 137)(120 138)(121 139)(122 140)(123 141)(124 142)(125 143)(126 144)
(1 71)(2 72)(3 37)(4 38)(5 39)(6 40)(7 41)(8 42)(9 43)(10 44)(11 45)(12 46)(13 47)(14 48)(15 49)(16 50)(17 51)(18 52)(19 53)(20 54)(21 55)(22 56)(23 57)(24 58)(25 59)(26 60)(27 61)(28 62)(29 63)(30 64)(31 65)(32 66)(33 67)(34 68)(35 69)(36 70)(73 110)(74 111)(75 112)(76 113)(77 114)(78 115)(79 116)(80 117)(81 118)(82 119)(83 120)(84 121)(85 122)(86 123)(87 124)(88 125)(89 126)(90 127)(91 128)(92 129)(93 130)(94 131)(95 132)(96 133)(97 134)(98 135)(99 136)(100 137)(101 138)(102 139)(103 140)(104 141)(105 142)(106 143)(107 144)(108 109)
(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)
(1 18 19 36)(2 35 20 17)(3 16 21 34)(4 33 22 15)(5 14 23 32)(6 31 24 13)(7 12 25 30)(8 29 26 11)(9 10 27 28)(37 50 55 68)(38 67 56 49)(39 48 57 66)(40 65 58 47)(41 46 59 64)(42 63 60 45)(43 44 61 62)(51 72 69 54)(52 53 70 71)(73 92 91 74)(75 90 93 108)(76 107 94 89)(77 88 95 106)(78 105 96 87)(79 86 97 104)(80 103 98 85)(81 84 99 102)(82 101 100 83)(109 112 127 130)(110 129 128 111)(113 144 131 126)(114 125 132 143)(115 142 133 124)(116 123 134 141)(117 140 135 122)(118 121 136 139)(119 138 137 120)
G:=sub<Sym(144)| (1,138)(2,102)(3,140)(4,104)(5,142)(6,106)(7,144)(8,108)(9,110)(10,74)(11,112)(12,76)(13,114)(14,78)(15,116)(16,80)(17,118)(18,82)(19,120)(20,84)(21,122)(22,86)(23,124)(24,88)(25,126)(26,90)(27,128)(28,92)(29,130)(30,94)(31,132)(32,96)(33,134)(34,98)(35,136)(36,100)(37,103)(38,141)(39,105)(40,143)(41,107)(42,109)(43,73)(44,111)(45,75)(46,113)(47,77)(48,115)(49,79)(50,117)(51,81)(52,119)(53,83)(54,121)(55,85)(56,123)(57,87)(58,125)(59,89)(60,127)(61,91)(62,129)(63,93)(64,131)(65,95)(66,133)(67,97)(68,135)(69,99)(70,137)(71,101)(72,139), (1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,99)(82,100)(83,101)(84,102)(85,103)(86,104)(87,105)(88,106)(89,107)(90,108)(109,127)(110,128)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144), (1,71)(2,72)(3,37)(4,38)(5,39)(6,40)(7,41)(8,42)(9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,57)(24,58)(25,59)(26,60)(27,61)(28,62)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,121)(85,122)(86,123)(87,124)(88,125)(89,126)(90,127)(91,128)(92,129)(93,130)(94,131)(95,132)(96,133)(97,134)(98,135)(99,136)(100,137)(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,109), (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), (1,18,19,36)(2,35,20,17)(3,16,21,34)(4,33,22,15)(5,14,23,32)(6,31,24,13)(7,12,25,30)(8,29,26,11)(9,10,27,28)(37,50,55,68)(38,67,56,49)(39,48,57,66)(40,65,58,47)(41,46,59,64)(42,63,60,45)(43,44,61,62)(51,72,69,54)(52,53,70,71)(73,92,91,74)(75,90,93,108)(76,107,94,89)(77,88,95,106)(78,105,96,87)(79,86,97,104)(80,103,98,85)(81,84,99,102)(82,101,100,83)(109,112,127,130)(110,129,128,111)(113,144,131,126)(114,125,132,143)(115,142,133,124)(116,123,134,141)(117,140,135,122)(118,121,136,139)(119,138,137,120)>;
G:=Group( (1,138)(2,102)(3,140)(4,104)(5,142)(6,106)(7,144)(8,108)(9,110)(10,74)(11,112)(12,76)(13,114)(14,78)(15,116)(16,80)(17,118)(18,82)(19,120)(20,84)(21,122)(22,86)(23,124)(24,88)(25,126)(26,90)(27,128)(28,92)(29,130)(30,94)(31,132)(32,96)(33,134)(34,98)(35,136)(36,100)(37,103)(38,141)(39,105)(40,143)(41,107)(42,109)(43,73)(44,111)(45,75)(46,113)(47,77)(48,115)(49,79)(50,117)(51,81)(52,119)(53,83)(54,121)(55,85)(56,123)(57,87)(58,125)(59,89)(60,127)(61,91)(62,129)(63,93)(64,131)(65,95)(66,133)(67,97)(68,135)(69,99)(70,137)(71,101)(72,139), (1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(73,91)(74,92)(75,93)(76,94)(77,95)(78,96)(79,97)(80,98)(81,99)(82,100)(83,101)(84,102)(85,103)(86,104)(87,105)(88,106)(89,107)(90,108)(109,127)(110,128)(111,129)(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144), (1,71)(2,72)(3,37)(4,38)(5,39)(6,40)(7,41)(8,42)(9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,57)(24,58)(25,59)(26,60)(27,61)(28,62)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)(73,110)(74,111)(75,112)(76,113)(77,114)(78,115)(79,116)(80,117)(81,118)(82,119)(83,120)(84,121)(85,122)(86,123)(87,124)(88,125)(89,126)(90,127)(91,128)(92,129)(93,130)(94,131)(95,132)(96,133)(97,134)(98,135)(99,136)(100,137)(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,109), (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), (1,18,19,36)(2,35,20,17)(3,16,21,34)(4,33,22,15)(5,14,23,32)(6,31,24,13)(7,12,25,30)(8,29,26,11)(9,10,27,28)(37,50,55,68)(38,67,56,49)(39,48,57,66)(40,65,58,47)(41,46,59,64)(42,63,60,45)(43,44,61,62)(51,72,69,54)(52,53,70,71)(73,92,91,74)(75,90,93,108)(76,107,94,89)(77,88,95,106)(78,105,96,87)(79,86,97,104)(80,103,98,85)(81,84,99,102)(82,101,100,83)(109,112,127,130)(110,129,128,111)(113,144,131,126)(114,125,132,143)(115,142,133,124)(116,123,134,141)(117,140,135,122)(118,121,136,139)(119,138,137,120) );
G=PermutationGroup([[(1,138),(2,102),(3,140),(4,104),(5,142),(6,106),(7,144),(8,108),(9,110),(10,74),(11,112),(12,76),(13,114),(14,78),(15,116),(16,80),(17,118),(18,82),(19,120),(20,84),(21,122),(22,86),(23,124),(24,88),(25,126),(26,90),(27,128),(28,92),(29,130),(30,94),(31,132),(32,96),(33,134),(34,98),(35,136),(36,100),(37,103),(38,141),(39,105),(40,143),(41,107),(42,109),(43,73),(44,111),(45,75),(46,113),(47,77),(48,115),(49,79),(50,117),(51,81),(52,119),(53,83),(54,121),(55,85),(56,123),(57,87),(58,125),(59,89),(60,127),(61,91),(62,129),(63,93),(64,131),(65,95),(66,133),(67,97),(68,135),(69,99),(70,137),(71,101),(72,139)], [(1,19),(2,20),(3,21),(4,22),(5,23),(6,24),(7,25),(8,26),(9,27),(10,28),(11,29),(12,30),(13,31),(14,32),(15,33),(16,34),(17,35),(18,36),(37,55),(38,56),(39,57),(40,58),(41,59),(42,60),(43,61),(44,62),(45,63),(46,64),(47,65),(48,66),(49,67),(50,68),(51,69),(52,70),(53,71),(54,72),(73,91),(74,92),(75,93),(76,94),(77,95),(78,96),(79,97),(80,98),(81,99),(82,100),(83,101),(84,102),(85,103),(86,104),(87,105),(88,106),(89,107),(90,108),(109,127),(110,128),(111,129),(112,130),(113,131),(114,132),(115,133),(116,134),(117,135),(118,136),(119,137),(120,138),(121,139),(122,140),(123,141),(124,142),(125,143),(126,144)], [(1,71),(2,72),(3,37),(4,38),(5,39),(6,40),(7,41),(8,42),(9,43),(10,44),(11,45),(12,46),(13,47),(14,48),(15,49),(16,50),(17,51),(18,52),(19,53),(20,54),(21,55),(22,56),(23,57),(24,58),(25,59),(26,60),(27,61),(28,62),(29,63),(30,64),(31,65),(32,66),(33,67),(34,68),(35,69),(36,70),(73,110),(74,111),(75,112),(76,113),(77,114),(78,115),(79,116),(80,117),(81,118),(82,119),(83,120),(84,121),(85,122),(86,123),(87,124),(88,125),(89,126),(90,127),(91,128),(92,129),(93,130),(94,131),(95,132),(96,133),(97,134),(98,135),(99,136),(100,137),(101,138),(102,139),(103,140),(104,141),(105,142),(106,143),(107,144),(108,109)], [(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)], [(1,18,19,36),(2,35,20,17),(3,16,21,34),(4,33,22,15),(5,14,23,32),(6,31,24,13),(7,12,25,30),(8,29,26,11),(9,10,27,28),(37,50,55,68),(38,67,56,49),(39,48,57,66),(40,65,58,47),(41,46,59,64),(42,63,60,45),(43,44,61,62),(51,72,69,54),(52,53,70,71),(73,92,91,74),(75,90,93,108),(76,107,94,89),(77,88,95,106),(78,105,96,87),(79,86,97,104),(80,103,98,85),(81,84,99,102),(82,101,100,83),(109,112,127,130),(110,129,128,111),(113,144,131,126),(114,125,132,143),(115,142,133,124),(116,123,134,141),(117,140,135,122),(118,121,136,139),(119,138,137,120)]])
54 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 6A | 6B | 6C | 6D | 6E | 9A | 9B | 9C | 12A | 12B | 12C | 12D | 18A | ··· | 18I | 18J | ··· | 18O | 36A | ··· | 36L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 6 | 6 | 9 | 9 | 9 | 12 | 12 | 12 | 12 | 18 | ··· | 18 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | 1 | 1 | 4 | 18 | 18 | 2 | 2 | 2 | 4 | 18 | 18 | 36 | 36 | 2 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
54 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | D6 | D6 | C4○D4 | D9 | D18 | D18 | C4○D12 | D36⋊5C2 | S3×D4 | D4⋊2S3 | D4×D9 | D4⋊2D9 |
| kernel | C23.9D18 | Dic9⋊C4 | C4⋊Dic9 | D18⋊C4 | C18.D4 | C9×C22⋊C4 | C2×C4×D9 | C2×C9⋊D4 | C3×C22⋊C4 | D18 | C2×C12 | C22×C6 | C18 | C22⋊C4 | C2×C4 | C23 | C6 | C2 | C6 | C6 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 4 | 3 | 6 | 3 | 4 | 12 | 1 | 1 | 3 | 3 |
Matrix representation of C23.9D18 ►in GL6(𝔽37)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 0 | 0 | 36 |
| 1 | 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 | 36 | 0 |
| 0 | 0 | 0 | 0 | 0 | 36 |
| 11 | 20 | 0 | 0 | 0 | 0 |
| 17 | 31 | 0 | 0 | 0 | 0 |
| 0 | 0 | 31 | 0 | 0 | 0 |
| 0 | 0 | 0 | 31 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 0 |
| 0 | 0 | 0 | 0 | 0 | 31 |
| 17 | 31 | 0 | 0 | 0 | 0 |
| 11 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 31 | 0 | 0 | 0 |
| 0 | 0 | 0 | 6 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 0 |
| 0 | 0 | 0 | 0 | 0 | 6 |
G:=sub<GL(6,GF(37))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,36],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,36,0,0,0,0,0,0,36],[11,17,0,0,0,0,20,31,0,0,0,0,0,0,31,0,0,0,0,0,0,31,0,0,0,0,0,0,6,0,0,0,0,0,0,31],[17,11,0,0,0,0,31,20,0,0,0,0,0,0,31,0,0,0,0,0,0,6,0,0,0,0,0,0,6,0,0,0,0,0,0,6] >;
C23.9D18 in GAP, Magma, Sage, TeX
C_2^3._9D_{18} % in TeX
G:=Group("C2^3.9D18"); // GroupNames label
G:=SmallGroup(288,93);
// by ID
G=gap.SmallGroup(288,93);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,64,254,219,6725,292,9414]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^2=1,d^18=e^2=b,a*b=b*a,d*a*d^-1=a*c=c*a,e*a*e^-1=a*b*c,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^17>;
// generators/relations