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, C4, C4, C6, C8, Q8, Q8, C32, Dic3, C12, C12, Q16, C3×C6, C3⋊C8, Dic6, C3×Q8, C3⋊Dic3, C3×C12, C3×C12, C3⋊Q16, C32⋊4C8, C32⋊4Q8, Q8×C32, C32⋊7Q16
Quotients: C1, C2, C22, S3, D4, D6, Q16, C3⋊S3, C3⋊D4, C2×C3⋊S3, C3⋊Q16, 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
(1 133 22)(2 23 134)(3 135 24)(4 17 136)(5 129 18)(6 19 130)(7 131 20)(8 21 132)(9 124 77)(10 78 125)(11 126 79)(12 80 127)(13 128 73)(14 74 121)(15 122 75)(16 76 123)(25 82 35)(26 36 83)(27 84 37)(28 38 85)(29 86 39)(30 40 87)(31 88 33)(32 34 81)(41 98 112)(42 105 99)(43 100 106)(44 107 101)(45 102 108)(46 109 103)(47 104 110)(48 111 97)(49 70 117)(50 118 71)(51 72 119)(52 120 65)(53 66 113)(54 114 67)(55 68 115)(56 116 69)(57 137 95)(58 96 138)(59 139 89)(60 90 140)(61 141 91)(62 92 142)(63 143 93)(64 94 144)
(1 15 117)(2 118 16)(3 9 119)(4 120 10)(5 11 113)(6 114 12)(7 13 115)(8 116 14)(17 65 78)(18 79 66)(19 67 80)(20 73 68)(21 69 74)(22 75 70)(23 71 76)(24 77 72)(25 89 110)(26 111 90)(27 91 112)(28 105 92)(29 93 106)(30 107 94)(31 95 108)(32 109 96)(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 84 61)(42 62 85)(43 86 63)(44 64 87)(45 88 57)(46 58 81)(47 82 59)(48 60 83)(49 133 122)(50 123 134)(51 135 124)(52 125 136)(53 129 126)(54 127 130)(55 131 128)(56 121 132)
(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 47 13 43)(10 46 14 42)(11 45 15 41)(12 44 16 48)(17 96 21 92)(18 95 22 91)(19 94 23 90)(20 93 24 89)(25 68 29 72)(26 67 30 71)(27 66 31 70)(28 65 32 69)(33 49 37 53)(34 56 38 52)(35 55 39 51)(36 54 40 50)(73 106 77 110)(74 105 78 109)(75 112 79 108)(76 111 80 107)(81 116 85 120)(82 115 86 119)(83 114 87 118)(84 113 88 117)(97 127 101 123)(98 126 102 122)(99 125 103 121)(100 124 104 128)(129 137 133 141)(130 144 134 140)(131 143 135 139)(132 142 136 138)
G:=sub<Sym(144)| (1,133,22)(2,23,134)(3,135,24)(4,17,136)(5,129,18)(6,19,130)(7,131,20)(8,21,132)(9,124,77)(10,78,125)(11,126,79)(12,80,127)(13,128,73)(14,74,121)(15,122,75)(16,76,123)(25,82,35)(26,36,83)(27,84,37)(28,38,85)(29,86,39)(30,40,87)(31,88,33)(32,34,81)(41,98,112)(42,105,99)(43,100,106)(44,107,101)(45,102,108)(46,109,103)(47,104,110)(48,111,97)(49,70,117)(50,118,71)(51,72,119)(52,120,65)(53,66,113)(54,114,67)(55,68,115)(56,116,69)(57,137,95)(58,96,138)(59,139,89)(60,90,140)(61,141,91)(62,92,142)(63,143,93)(64,94,144), (1,15,117)(2,118,16)(3,9,119)(4,120,10)(5,11,113)(6,114,12)(7,13,115)(8,116,14)(17,65,78)(18,79,66)(19,67,80)(20,73,68)(21,69,74)(22,75,70)(23,71,76)(24,77,72)(25,89,110)(26,111,90)(27,91,112)(28,105,92)(29,93,106)(30,107,94)(31,95,108)(32,109,96)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,84,61)(42,62,85)(43,86,63)(44,64,87)(45,88,57)(46,58,81)(47,82,59)(48,60,83)(49,133,122)(50,123,134)(51,135,124)(52,125,136)(53,129,126)(54,127,130)(55,131,128)(56,121,132), (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)(9,47,13,43)(10,46,14,42)(11,45,15,41)(12,44,16,48)(17,96,21,92)(18,95,22,91)(19,94,23,90)(20,93,24,89)(25,68,29,72)(26,67,30,71)(27,66,31,70)(28,65,32,69)(33,49,37,53)(34,56,38,52)(35,55,39,51)(36,54,40,50)(73,106,77,110)(74,105,78,109)(75,112,79,108)(76,111,80,107)(81,116,85,120)(82,115,86,119)(83,114,87,118)(84,113,88,117)(97,127,101,123)(98,126,102,122)(99,125,103,121)(100,124,104,128)(129,137,133,141)(130,144,134,140)(131,143,135,139)(132,142,136,138)>;
G:=Group( (1,133,22)(2,23,134)(3,135,24)(4,17,136)(5,129,18)(6,19,130)(7,131,20)(8,21,132)(9,124,77)(10,78,125)(11,126,79)(12,80,127)(13,128,73)(14,74,121)(15,122,75)(16,76,123)(25,82,35)(26,36,83)(27,84,37)(28,38,85)(29,86,39)(30,40,87)(31,88,33)(32,34,81)(41,98,112)(42,105,99)(43,100,106)(44,107,101)(45,102,108)(46,109,103)(47,104,110)(48,111,97)(49,70,117)(50,118,71)(51,72,119)(52,120,65)(53,66,113)(54,114,67)(55,68,115)(56,116,69)(57,137,95)(58,96,138)(59,139,89)(60,90,140)(61,141,91)(62,92,142)(63,143,93)(64,94,144), (1,15,117)(2,118,16)(3,9,119)(4,120,10)(5,11,113)(6,114,12)(7,13,115)(8,116,14)(17,65,78)(18,79,66)(19,67,80)(20,73,68)(21,69,74)(22,75,70)(23,71,76)(24,77,72)(25,89,110)(26,111,90)(27,91,112)(28,105,92)(29,93,106)(30,107,94)(31,95,108)(32,109,96)(33,137,102)(34,103,138)(35,139,104)(36,97,140)(37,141,98)(38,99,142)(39,143,100)(40,101,144)(41,84,61)(42,62,85)(43,86,63)(44,64,87)(45,88,57)(46,58,81)(47,82,59)(48,60,83)(49,133,122)(50,123,134)(51,135,124)(52,125,136)(53,129,126)(54,127,130)(55,131,128)(56,121,132), (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)(9,47,13,43)(10,46,14,42)(11,45,15,41)(12,44,16,48)(17,96,21,92)(18,95,22,91)(19,94,23,90)(20,93,24,89)(25,68,29,72)(26,67,30,71)(27,66,31,70)(28,65,32,69)(33,49,37,53)(34,56,38,52)(35,55,39,51)(36,54,40,50)(73,106,77,110)(74,105,78,109)(75,112,79,108)(76,111,80,107)(81,116,85,120)(82,115,86,119)(83,114,87,118)(84,113,88,117)(97,127,101,123)(98,126,102,122)(99,125,103,121)(100,124,104,128)(129,137,133,141)(130,144,134,140)(131,143,135,139)(132,142,136,138) );
G=PermutationGroup([[(1,133,22),(2,23,134),(3,135,24),(4,17,136),(5,129,18),(6,19,130),(7,131,20),(8,21,132),(9,124,77),(10,78,125),(11,126,79),(12,80,127),(13,128,73),(14,74,121),(15,122,75),(16,76,123),(25,82,35),(26,36,83),(27,84,37),(28,38,85),(29,86,39),(30,40,87),(31,88,33),(32,34,81),(41,98,112),(42,105,99),(43,100,106),(44,107,101),(45,102,108),(46,109,103),(47,104,110),(48,111,97),(49,70,117),(50,118,71),(51,72,119),(52,120,65),(53,66,113),(54,114,67),(55,68,115),(56,116,69),(57,137,95),(58,96,138),(59,139,89),(60,90,140),(61,141,91),(62,92,142),(63,143,93),(64,94,144)], [(1,15,117),(2,118,16),(3,9,119),(4,120,10),(5,11,113),(6,114,12),(7,13,115),(8,116,14),(17,65,78),(18,79,66),(19,67,80),(20,73,68),(21,69,74),(22,75,70),(23,71,76),(24,77,72),(25,89,110),(26,111,90),(27,91,112),(28,105,92),(29,93,106),(30,107,94),(31,95,108),(32,109,96),(33,137,102),(34,103,138),(35,139,104),(36,97,140),(37,141,98),(38,99,142),(39,143,100),(40,101,144),(41,84,61),(42,62,85),(43,86,63),(44,64,87),(45,88,57),(46,58,81),(47,82,59),(48,60,83),(49,133,122),(50,123,134),(51,135,124),(52,125,136),(53,129,126),(54,127,130),(55,131,128),(56,121,132)], [(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),(9,47,13,43),(10,46,14,42),(11,45,15,41),(12,44,16,48),(17,96,21,92),(18,95,22,91),(19,94,23,90),(20,93,24,89),(25,68,29,72),(26,67,30,71),(27,66,31,70),(28,65,32,69),(33,49,37,53),(34,56,38,52),(35,55,39,51),(36,54,40,50),(73,106,77,110),(74,105,78,109),(75,112,79,108),(76,111,80,107),(81,116,85,120),(82,115,86,119),(83,114,87,118),(84,113,88,117),(97,127,101,123),(98,126,102,122),(99,125,103,121),(100,124,104,128),(129,137,133,141),(130,144,134,140),(131,143,135,139),(132,142,136,138)]])
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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