metabelian, supersoluble, monomial
Aliases: C32⋊7Q16, C12.19D6, (C3×C6).37D4, (C3×Q8).9S3, C3⋊3(C3⋊Q16), Q8.2(C3⋊S3), C6.25(C3⋊D4), C32⋊4C8.2C2, (Q8×C32).2C2, C32⋊4Q8.3C2, (C3×C12).15C22, C2.7(C32⋊7D4), C4.4(C2×C3⋊S3), SmallGroup(144,99)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C32⋊7Q16
G = < a,b,c,d | a3=b3=c8=1, d2=c4, ab=ba, cac-1=a-1, ad=da, cbc-1=b-1, bd=db, dcd-1=c-1 >
Subgroups: 146 in 54 conjugacy classes, 27 normal (11 characteristic)
C1, C2, C3 [×4], C4, C4 [×2], C6 [×4], C8, Q8, Q8, C32, Dic3 [×4], C12 [×4], C12 [×4], Q16, C3×C6, C3⋊C8 [×4], Dic6 [×4], C3×Q8 [×4], C3⋊Dic3, C3×C12, C3×C12, C3⋊Q16 [×4], C32⋊4C8, C32⋊4Q8, Q8×C32, C32⋊7Q16
Quotients: C1, C2 [×3], C22, S3 [×4], D4, D6 [×4], Q16, C3⋊S3, C3⋊D4 [×4], C2×C3⋊S3, C3⋊Q16 [×4], C32⋊7D4, C32⋊7Q16
Character table of C32⋊7Q16
| class | 1 | 2 | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 6A | 6B | 6C | 6D | 8A | 8B | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | 12I | 12J | 12K | 12L | |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 36 | 2 | 2 | 2 | 2 | 18 | 18 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | linear of order 2 |
| ρ4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | linear of order 2 |
| ρ5 | 2 | 2 | -1 | -1 | 2 | -1 | 2 | 2 | 0 | -1 | 2 | -1 | -1 | 0 | 0 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ6 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 2 | 0 | -1 | -1 | 2 | -1 | 0 | 0 | -1 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | orthogonal lifted from S3 |
| ρ7 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | -2 | 0 | -1 | -1 | 2 | -1 | 0 | 0 | -1 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | 2 | -1 | -1 | orthogonal lifted from D6 |
| ρ8 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 0 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 2 | -1 | 2 | -1 | -1 | -1 | 2 | orthogonal lifted from S3 |
| ρ9 | 2 | 2 | -1 | -1 | 2 | -1 | 2 | -2 | 0 | -1 | 2 | -1 | -1 | 0 | 0 | 2 | -2 | -2 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ10 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | -2 | 0 | 2 | -1 | -1 | -1 | 0 | 0 | -1 | 1 | 1 | 1 | 1 | -2 | 1 | -2 | 1 | -1 | -1 | 2 | orthogonal lifted from D6 |
| ρ11 | 2 | 2 | -1 | 2 | -1 | -1 | 2 | -2 | 0 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | 1 | 1 | 1 | -2 | 1 | 1 | 1 | -2 | -1 | 2 | -1 | orthogonal lifted from D6 |
| ρ12 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | 2 | 2 | 2 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | -1 | 2 | -1 | -1 | 2 | 2 | 0 | -1 | -1 | -1 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | 2 | -1 | 2 | -1 | orthogonal lifted from S3 |
| ρ14 | 2 | -2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | -√2 | √2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q16, Schur index 2 |
| ρ15 | 2 | -2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | √2 | -√2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q16, Schur index 2 |
| ρ16 | 2 | 2 | -1 | 2 | -1 | -1 | -2 | 0 | 0 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | -√-3 | √-3 | √-3 | 0 | -√-3 | -√-3 | √-3 | 0 | 1 | -2 | 1 | complex lifted from C3⋊D4 |
| ρ17 | 2 | 2 | 2 | -1 | -1 | -1 | -2 | 0 | 0 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | √-3 | -√-3 | √-3 | -√-3 | 0 | -√-3 | 0 | √-3 | 1 | 1 | -2 | complex lifted from C3⋊D4 |
| ρ18 | 2 | 2 | -1 | -1 | 2 | -1 | -2 | 0 | 0 | -1 | 2 | -1 | -1 | 0 | 0 | -2 | 0 | 0 | -√-3 | -√-3 | -√-3 | √-3 | √-3 | √-3 | 1 | 1 | 1 | complex lifted from C3⋊D4 |
| ρ19 | 2 | 2 | -1 | -1 | -1 | 2 | -2 | 0 | 0 | -1 | -1 | 2 | -1 | 0 | 0 | 1 | -√-3 | √-3 | 0 | -√-3 | √-3 | 0 | -√-3 | √-3 | -2 | 1 | 1 | complex lifted from C3⋊D4 |
| ρ20 | 2 | 2 | -1 | 2 | -1 | -1 | -2 | 0 | 0 | -1 | -1 | -1 | 2 | 0 | 0 | 1 | √-3 | -√-3 | -√-3 | 0 | √-3 | √-3 | -√-3 | 0 | 1 | -2 | 1 | complex lifted from C3⋊D4 |
| ρ21 | 2 | 2 | -1 | -1 | -1 | 2 | -2 | 0 | 0 | -1 | -1 | 2 | -1 | 0 | 0 | 1 | √-3 | -√-3 | 0 | √-3 | -√-3 | 0 | √-3 | -√-3 | -2 | 1 | 1 | complex lifted from C3⋊D4 |
| ρ22 | 2 | 2 | 2 | -1 | -1 | -1 | -2 | 0 | 0 | 2 | -1 | -1 | -1 | 0 | 0 | 1 | -√-3 | √-3 | -√-3 | √-3 | 0 | √-3 | 0 | -√-3 | 1 | 1 | -2 | complex lifted from C3⋊D4 |
| ρ23 | 2 | 2 | -1 | -1 | 2 | -1 | -2 | 0 | 0 | -1 | 2 | -1 | -1 | 0 | 0 | -2 | 0 | 0 | √-3 | √-3 | √-3 | -√-3 | -√-3 | -√-3 | 1 | 1 | 1 | complex lifted from C3⋊D4 |
| ρ24 | 4 | -4 | -2 | 4 | -2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C3⋊Q16, Schur index 2 |
| ρ25 | 4 | -4 | -2 | -2 | 4 | -2 | 0 | 0 | 0 | 2 | -4 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C3⋊Q16, Schur index 2 |
| ρ26 | 4 | -4 | 4 | -2 | -2 | -2 | 0 | 0 | 0 | -4 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C3⋊Q16, Schur index 2 |
| ρ27 | 4 | -4 | -2 | -2 | -2 | 4 | 0 | 0 | 0 | 2 | 2 | -4 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C3⋊Q16, Schur index 2 |
►Regular action on 144 points
Generators in S144
(1 72 11)(2 12 65)(3 66 13)(4 14 67)(5 68 15)(6 16 69)(7 70 9)(8 10 71)(17 123 107)(18 108 124)(19 125 109)(20 110 126)(21 127 111)(22 112 128)(23 121 105)(24 106 122)(25 44 91)(26 92 45)(27 46 93)(28 94 47)(29 48 95)(30 96 41)(31 42 89)(32 90 43)(33 113 79)(34 80 114)(35 115 73)(36 74 116)(37 117 75)(38 76 118)(39 119 77)(40 78 120)(49 144 64)(50 57 137)(51 138 58)(52 59 139)(53 140 60)(54 61 141)(55 142 62)(56 63 143)(81 134 101)(82 102 135)(83 136 103)(84 104 129)(85 130 97)(86 98 131)(87 132 99)(88 100 133)
(1 106 31)(2 32 107)(3 108 25)(4 26 109)(5 110 27)(6 28 111)(7 112 29)(8 30 105)(9 22 95)(10 96 23)(11 24 89)(12 90 17)(13 18 91)(14 92 19)(15 20 93)(16 94 21)(33 137 102)(34 103 138)(35 139 104)(36 97 140)(37 141 98)(38 99 142)(39 143 100)(40 101 144)(41 121 71)(42 72 122)(43 123 65)(44 66 124)(45 125 67)(46 68 126)(47 127 69)(48 70 128)(49 120 134)(50 135 113)(51 114 136)(52 129 115)(53 116 130)(54 131 117)(55 118 132)(56 133 119)(57 82 79)(58 80 83)(59 84 73)(60 74 85)(61 86 75)(62 76 87)(63 88 77)(64 78 81)
(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 61 5 57)(2 60 6 64)(3 59 7 63)(4 58 8 62)(9 56 13 52)(10 55 14 51)(11 54 15 50)(12 53 16 49)(17 130 21 134)(18 129 22 133)(19 136 23 132)(20 135 24 131)(25 73 29 77)(26 80 30 76)(27 79 31 75)(28 78 32 74)(33 42 37 46)(34 41 38 45)(35 48 39 44)(36 47 40 43)(65 140 69 144)(66 139 70 143)(67 138 71 142)(68 137 72 141)(81 107 85 111)(82 106 86 110)(83 105 87 109)(84 112 88 108)(89 117 93 113)(90 116 94 120)(91 115 95 119)(92 114 96 118)(97 127 101 123)(98 126 102 122)(99 125 103 121)(100 124 104 128)
G:=sub<Sym(144)| (1,72,11)(2,12,65)(3,66,13)(4,14,67)(5,68,15)(6,16,69)(7,70,9)(8,10,71)(17,123,107)(18,108,124)(19,125,109)(20,110,126)(21,127,111)(22,112,128)(23,121,105)(24,106,122)(25,44,91)(26,92,45)(27,46,93)(28,94,47)(29,48,95)(30,96,41)(31,42,89)(32,90,43)(33,113,79)(34,80,114)(35,115,73)(36,74,116)(37,117,75)(38,76,118)(39,119,77)(40,78,120)(49,144,64)(50,57,137)(51,138,58)(52,59,139)(53,140,60)(54,61,141)(55,142,62)(56,63,143)(81,134,101)(82,102,135)(83,136,103)(84,104,129)(85,130,97)(86,98,131)(87,132,99)(88,100,133), (1,106,31)(2,32,107)(3,108,25)(4,26,109)(5,110,27)(6,28,111)(7,112,29)(8,30,105)(9,22,95)(10,96,23)(11,24,89)(12,90,17)(13,18,91)(14,92,19)(15,20,93)(16,94,21)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,121,71)(42,72,122)(43,123,65)(44,66,124)(45,125,67)(46,68,126)(47,127,69)(48,70,128)(49,120,134)(50,135,113)(51,114,136)(52,129,115)(53,116,130)(54,131,117)(55,118,132)(56,133,119)(57,82,79)(58,80,83)(59,84,73)(60,74,85)(61,86,75)(62,76,87)(63,88,77)(64,78,81), (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), (1,61,5,57)(2,60,6,64)(3,59,7,63)(4,58,8,62)(9,56,13,52)(10,55,14,51)(11,54,15,50)(12,53,16,49)(17,130,21,134)(18,129,22,133)(19,136,23,132)(20,135,24,131)(25,73,29,77)(26,80,30,76)(27,79,31,75)(28,78,32,74)(33,42,37,46)(34,41,38,45)(35,48,39,44)(36,47,40,43)(65,140,69,144)(66,139,70,143)(67,138,71,142)(68,137,72,141)(81,107,85,111)(82,106,86,110)(83,105,87,109)(84,112,88,108)(89,117,93,113)(90,116,94,120)(91,115,95,119)(92,114,96,118)(97,127,101,123)(98,126,102,122)(99,125,103,121)(100,124,104,128)>;
G:=Group( (1,72,11)(2,12,65)(3,66,13)(4,14,67)(5,68,15)(6,16,69)(7,70,9)(8,10,71)(17,123,107)(18,108,124)(19,125,109)(20,110,126)(21,127,111)(22,112,128)(23,121,105)(24,106,122)(25,44,91)(26,92,45)(27,46,93)(28,94,47)(29,48,95)(30,96,41)(31,42,89)(32,90,43)(33,113,79)(34,80,114)(35,115,73)(36,74,116)(37,117,75)(38,76,118)(39,119,77)(40,78,120)(49,144,64)(50,57,137)(51,138,58)(52,59,139)(53,140,60)(54,61,141)(55,142,62)(56,63,143)(81,134,101)(82,102,135)(83,136,103)(84,104,129)(85,130,97)(86,98,131)(87,132,99)(88,100,133), (1,106,31)(2,32,107)(3,108,25)(4,26,109)(5,110,27)(6,28,111)(7,112,29)(8,30,105)(9,22,95)(10,96,23)(11,24,89)(12,90,17)(13,18,91)(14,92,19)(15,20,93)(16,94,21)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,121,71)(42,72,122)(43,123,65)(44,66,124)(45,125,67)(46,68,126)(47,127,69)(48,70,128)(49,120,134)(50,135,113)(51,114,136)(52,129,115)(53,116,130)(54,131,117)(55,118,132)(56,133,119)(57,82,79)(58,80,83)(59,84,73)(60,74,85)(61,86,75)(62,76,87)(63,88,77)(64,78,81), (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), (1,61,5,57)(2,60,6,64)(3,59,7,63)(4,58,8,62)(9,56,13,52)(10,55,14,51)(11,54,15,50)(12,53,16,49)(17,130,21,134)(18,129,22,133)(19,136,23,132)(20,135,24,131)(25,73,29,77)(26,80,30,76)(27,79,31,75)(28,78,32,74)(33,42,37,46)(34,41,38,45)(35,48,39,44)(36,47,40,43)(65,140,69,144)(66,139,70,143)(67,138,71,142)(68,137,72,141)(81,107,85,111)(82,106,86,110)(83,105,87,109)(84,112,88,108)(89,117,93,113)(90,116,94,120)(91,115,95,119)(92,114,96,118)(97,127,101,123)(98,126,102,122)(99,125,103,121)(100,124,104,128) );
G=PermutationGroup([(1,72,11),(2,12,65),(3,66,13),(4,14,67),(5,68,15),(6,16,69),(7,70,9),(8,10,71),(17,123,107),(18,108,124),(19,125,109),(20,110,126),(21,127,111),(22,112,128),(23,121,105),(24,106,122),(25,44,91),(26,92,45),(27,46,93),(28,94,47),(29,48,95),(30,96,41),(31,42,89),(32,90,43),(33,113,79),(34,80,114),(35,115,73),(36,74,116),(37,117,75),(38,76,118),(39,119,77),(40,78,120),(49,144,64),(50,57,137),(51,138,58),(52,59,139),(53,140,60),(54,61,141),(55,142,62),(56,63,143),(81,134,101),(82,102,135),(83,136,103),(84,104,129),(85,130,97),(86,98,131),(87,132,99),(88,100,133)], [(1,106,31),(2,32,107),(3,108,25),(4,26,109),(5,110,27),(6,28,111),(7,112,29),(8,30,105),(9,22,95),(10,96,23),(11,24,89),(12,90,17),(13,18,91),(14,92,19),(15,20,93),(16,94,21),(33,137,102),(34,103,138),(35,139,104),(36,97,140),(37,141,98),(38,99,142),(39,143,100),(40,101,144),(41,121,71),(42,72,122),(43,123,65),(44,66,124),(45,125,67),(46,68,126),(47,127,69),(48,70,128),(49,120,134),(50,135,113),(51,114,136),(52,129,115),(53,116,130),(54,131,117),(55,118,132),(56,133,119),(57,82,79),(58,80,83),(59,84,73),(60,74,85),(61,86,75),(62,76,87),(63,88,77),(64,78,81)], [(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)], [(1,61,5,57),(2,60,6,64),(3,59,7,63),(4,58,8,62),(9,56,13,52),(10,55,14,51),(11,54,15,50),(12,53,16,49),(17,130,21,134),(18,129,22,133),(19,136,23,132),(20,135,24,131),(25,73,29,77),(26,80,30,76),(27,79,31,75),(28,78,32,74),(33,42,37,46),(34,41,38,45),(35,48,39,44),(36,47,40,43),(65,140,69,144),(66,139,70,143),(67,138,71,142),(68,137,72,141),(81,107,85,111),(82,106,86,110),(83,105,87,109),(84,112,88,108),(89,117,93,113),(90,116,94,120),(91,115,95,119),(92,114,96,118),(97,127,101,123),(98,126,102,122),(99,125,103,121),(100,124,104,128)])
C32⋊7Q16 is a maximal subgroup of
S3×C3⋊Q16 D12.11D6 D12.24D6 D12.12D6 C24.32D6 C24.40D6 Q16×C3⋊S3 C24.35D6 C62.134D4 C62.74D4 C62.75D4 He3⋊6Q16 C36.19D6 C32.3CSU2(𝔽3) C33⋊6Q16 C33⋊7Q16 C33⋊15Q16 C32⋊4CSU2(𝔽3)
C32⋊7Q16 is a maximal quotient of
C12.9Dic6 C62.114D4 C62.117D4 C36.19D6 He3⋊7Q16 C33⋊6Q16 C33⋊7Q16 C33⋊15Q16
Matrix representation of C32⋊7Q16 ►in GL6(𝔽73)
| 0 | 1 | 0 | 0 | 0 | 0 |
| 72 | 72 | 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 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 72 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 0 | 0 | 0 |
| 0 | 0 | 42 | 64 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 41 | 51 | 0 | 0 | 0 | 0 |
| 10 | 32 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 58 | 0 | 0 |
| 0 | 0 | 52 | 66 | 0 | 0 |
| 0 | 0 | 0 | 0 | 41 | 38 |
| 0 | 0 | 0 | 0 | 48 | 0 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 35 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 71 | 59 |
| 0 | 0 | 0 | 0 | 16 | 2 |
G:=sub<GL(6,GF(73))| [0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,72,0,0,0,0,1,72,0,0,0,0,0,0,8,42,0,0,0,0,0,64,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[41,10,0,0,0,0,51,32,0,0,0,0,0,0,7,52,0,0,0,0,58,66,0,0,0,0,0,0,41,48,0,0,0,0,38,0],[72,0,0,0,0,0,0,72,0,0,0,0,0,0,1,35,0,0,0,0,0,72,0,0,0,0,0,0,71,16,0,0,0,0,59,2] >;
C32⋊7Q16 in GAP, Magma, Sage, TeX
C_3^2\rtimes_7Q_{16} % in TeX
G:=Group("C3^2:7Q16"); // GroupNames label
G:=SmallGroup(144,99);
// by ID
G=gap.SmallGroup(144,99);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-3,48,73,55,218,116,50,964,3461]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^3=c^8=1,d^2=c^4,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
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