p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.255C23, C4⋊C4.77D4, (C2×C8).193D4, (C2×Q8).64D4, C8⋊4Q8.9C2, C8⋊2C8.11C2, C4⋊C8.37C22, C4.Q16.8C2, C4⋊Q8.76C22, C4.110(C4○D8), (C4×C8).288C22, Q8⋊Q8.11C2, C4.10D8.9C2, C4.6Q16.8C2, (C4×Q8).52C22, C2.11(C8.D4), C4.47(C8.C22), C4.SD16.13C2, C2.23(D4.3D4), C2.15(Q8.D4), C22.216(C4⋊D4), (C2×C4).40(C4○D4), (C2×C4).1290(C2×D4), SmallGroup(128,436)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.255C23
G = < a,b,c,d,e | a4=b4=1, c2=a2, d2=a-1b2, e2=b2, ab=ba, cac-1=a-1, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, dcd-1=a-1c, ece-1=bc, ede-1=a2d >
Subgroups: 144 in 70 conjugacy classes, 32 normal (all characteristic)
C1, C2 [×3], C4 [×4], C4 [×5], C22, C8 [×5], C2×C4 [×3], C2×C4 [×4], Q8 [×5], C42, C42, C4⋊C4, C4⋊C4 [×5], C2×C8 [×2], C2×C8 [×3], C2×Q8, C2×Q8 [×2], C4×C8, C8⋊C4, Q8⋊C4 [×4], C4⋊C8 [×3], C4⋊C8, C4.Q8, C2.D8, C4×Q8, C4⋊Q8 [×2], C4.10D8, C4.6Q16, C8⋊2C8, C8⋊4Q8, Q8⋊Q8, C4.Q16, C4.SD16, C42.255C23
Quotients: C1, C2 [×7], C22 [×7], D4 [×4], C23, C2×D4 [×2], C4○D4, C4⋊D4, C4○D8, C8.C22 [×3], Q8.D4, C8.D4, D4.3D4, C42.255C23
Character table of C42.255C23
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | 8J | |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 8 | 8 | 16 | 16 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | |
| ρ1 | 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 | 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 | 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 | linear of order 2 |
| ρ5 | 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 |
| ρ6 | 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 |
| ρ7 | 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 |
| ρ8 | 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 |
| ρ9 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ12 | 2 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2i | -2i | 0 | complex lifted from C4○D4 |
| ρ14 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2i | 2i | 0 | complex lifted from C4○D4 |
| ρ15 | 2 | -2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2i | 2i | 0 | √2 | -√-2 | -√2 | 0 | 0 | √-2 | complex lifted from C4○D8 |
| ρ16 | 2 | -2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2i | -2i | 0 | -√2 | -√-2 | √2 | 0 | 0 | √-2 | complex lifted from C4○D8 |
| ρ17 | 2 | -2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2i | 2i | 0 | -√2 | √-2 | √2 | 0 | 0 | -√-2 | complex lifted from C4○D8 |
| ρ18 | 2 | -2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2i | -2i | 0 | √2 | √-2 | -√2 | 0 | 0 | -√-2 | complex lifted from C4○D8 |
| ρ19 | 4 | -4 | -4 | 4 | 4 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ20 | 4 | -4 | 4 | -4 | 0 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ21 | 4 | -4 | 4 | -4 | 0 | 4 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ22 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√-2 | 0 | 0 | -2√-2 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D4.3D4 |
| ρ23 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√-2 | 0 | 0 | 2√-2 | 0 | 0 | 0 | 0 | 0 | 0 | complex lifted from D4.3D4 |
►Regular action on 128 points
Generators in S128
(1 24 5 20)(2 17 6 21)(3 18 7 22)(4 19 8 23)(9 41 13 45)(10 42 14 46)(11 43 15 47)(12 44 16 48)(25 49 29 53)(26 50 30 54)(27 51 31 55)(28 52 32 56)(33 122 37 126)(34 123 38 127)(35 124 39 128)(36 125 40 121)(57 74 61 78)(58 75 62 79)(59 76 63 80)(60 77 64 73)(65 104 69 100)(66 97 70 101)(67 98 71 102)(68 99 72 103)(81 94 85 90)(82 95 86 91)(83 96 87 92)(84 89 88 93)(105 113 109 117)(106 114 110 118)(107 115 111 119)(108 116 112 120)
(1 61 18 80)(2 62 19 73)(3 63 20 74)(4 64 21 75)(5 57 22 76)(6 58 23 77)(7 59 24 78)(8 60 17 79)(9 118 43 108)(10 119 44 109)(11 120 45 110)(12 113 46 111)(13 114 47 112)(14 115 48 105)(15 116 41 106)(16 117 42 107)(25 104 51 71)(26 97 52 72)(27 98 53 65)(28 99 54 66)(29 100 55 67)(30 101 56 68)(31 102 49 69)(32 103 50 70)(33 95 124 88)(34 96 125 81)(35 89 126 82)(36 90 127 83)(37 91 128 84)(38 92 121 85)(39 93 122 86)(40 94 123 87)
(1 90 5 94)(2 82 6 86)(3 96 7 92)(4 88 8 84)(9 71 13 67)(10 103 14 99)(11 69 15 65)(12 101 16 97)(17 91 21 95)(18 83 22 87)(19 89 23 93)(20 81 24 85)(25 112 29 108)(26 113 30 117)(27 110 31 106)(28 119 32 115)(33 79 37 75)(34 59 38 63)(35 77 39 73)(36 57 40 61)(41 98 45 102)(42 72 46 68)(43 104 47 100)(44 70 48 66)(49 116 53 120)(50 105 54 109)(51 114 55 118)(52 111 56 107)(58 122 62 126)(60 128 64 124)(74 125 78 121)(76 123 80 127)
(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)
(1 29 18 55)(2 26 19 52)(3 31 20 49)(4 28 21 54)(5 25 22 51)(6 30 23 56)(7 27 24 53)(8 32 17 50)(9 90 43 83)(10 95 44 88)(11 92 45 85)(12 89 46 82)(13 94 47 87)(14 91 48 84)(15 96 41 81)(16 93 42 86)(33 109 124 119)(34 106 125 116)(35 111 126 113)(36 108 127 118)(37 105 128 115)(38 110 121 120)(39 107 122 117)(40 112 123 114)(57 71 76 104)(58 68 77 101)(59 65 78 98)(60 70 79 103)(61 67 80 100)(62 72 73 97)(63 69 74 102)(64 66 75 99)
G:=sub<Sym(128)| (1,24,5,20)(2,17,6,21)(3,18,7,22)(4,19,8,23)(9,41,13,45)(10,42,14,46)(11,43,15,47)(12,44,16,48)(25,49,29,53)(26,50,30,54)(27,51,31,55)(28,52,32,56)(33,122,37,126)(34,123,38,127)(35,124,39,128)(36,125,40,121)(57,74,61,78)(58,75,62,79)(59,76,63,80)(60,77,64,73)(65,104,69,100)(66,97,70,101)(67,98,71,102)(68,99,72,103)(81,94,85,90)(82,95,86,91)(83,96,87,92)(84,89,88,93)(105,113,109,117)(106,114,110,118)(107,115,111,119)(108,116,112,120), (1,61,18,80)(2,62,19,73)(3,63,20,74)(4,64,21,75)(5,57,22,76)(6,58,23,77)(7,59,24,78)(8,60,17,79)(9,118,43,108)(10,119,44,109)(11,120,45,110)(12,113,46,111)(13,114,47,112)(14,115,48,105)(15,116,41,106)(16,117,42,107)(25,104,51,71)(26,97,52,72)(27,98,53,65)(28,99,54,66)(29,100,55,67)(30,101,56,68)(31,102,49,69)(32,103,50,70)(33,95,124,88)(34,96,125,81)(35,89,126,82)(36,90,127,83)(37,91,128,84)(38,92,121,85)(39,93,122,86)(40,94,123,87), (1,90,5,94)(2,82,6,86)(3,96,7,92)(4,88,8,84)(9,71,13,67)(10,103,14,99)(11,69,15,65)(12,101,16,97)(17,91,21,95)(18,83,22,87)(19,89,23,93)(20,81,24,85)(25,112,29,108)(26,113,30,117)(27,110,31,106)(28,119,32,115)(33,79,37,75)(34,59,38,63)(35,77,39,73)(36,57,40,61)(41,98,45,102)(42,72,46,68)(43,104,47,100)(44,70,48,66)(49,116,53,120)(50,105,54,109)(51,114,55,118)(52,111,56,107)(58,122,62,126)(60,128,64,124)(74,125,78,121)(76,123,80,127), (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), (1,29,18,55)(2,26,19,52)(3,31,20,49)(4,28,21,54)(5,25,22,51)(6,30,23,56)(7,27,24,53)(8,32,17,50)(9,90,43,83)(10,95,44,88)(11,92,45,85)(12,89,46,82)(13,94,47,87)(14,91,48,84)(15,96,41,81)(16,93,42,86)(33,109,124,119)(34,106,125,116)(35,111,126,113)(36,108,127,118)(37,105,128,115)(38,110,121,120)(39,107,122,117)(40,112,123,114)(57,71,76,104)(58,68,77,101)(59,65,78,98)(60,70,79,103)(61,67,80,100)(62,72,73,97)(63,69,74,102)(64,66,75,99)>;
G:=Group( (1,24,5,20)(2,17,6,21)(3,18,7,22)(4,19,8,23)(9,41,13,45)(10,42,14,46)(11,43,15,47)(12,44,16,48)(25,49,29,53)(26,50,30,54)(27,51,31,55)(28,52,32,56)(33,122,37,126)(34,123,38,127)(35,124,39,128)(36,125,40,121)(57,74,61,78)(58,75,62,79)(59,76,63,80)(60,77,64,73)(65,104,69,100)(66,97,70,101)(67,98,71,102)(68,99,72,103)(81,94,85,90)(82,95,86,91)(83,96,87,92)(84,89,88,93)(105,113,109,117)(106,114,110,118)(107,115,111,119)(108,116,112,120), (1,61,18,80)(2,62,19,73)(3,63,20,74)(4,64,21,75)(5,57,22,76)(6,58,23,77)(7,59,24,78)(8,60,17,79)(9,118,43,108)(10,119,44,109)(11,120,45,110)(12,113,46,111)(13,114,47,112)(14,115,48,105)(15,116,41,106)(16,117,42,107)(25,104,51,71)(26,97,52,72)(27,98,53,65)(28,99,54,66)(29,100,55,67)(30,101,56,68)(31,102,49,69)(32,103,50,70)(33,95,124,88)(34,96,125,81)(35,89,126,82)(36,90,127,83)(37,91,128,84)(38,92,121,85)(39,93,122,86)(40,94,123,87), (1,90,5,94)(2,82,6,86)(3,96,7,92)(4,88,8,84)(9,71,13,67)(10,103,14,99)(11,69,15,65)(12,101,16,97)(17,91,21,95)(18,83,22,87)(19,89,23,93)(20,81,24,85)(25,112,29,108)(26,113,30,117)(27,110,31,106)(28,119,32,115)(33,79,37,75)(34,59,38,63)(35,77,39,73)(36,57,40,61)(41,98,45,102)(42,72,46,68)(43,104,47,100)(44,70,48,66)(49,116,53,120)(50,105,54,109)(51,114,55,118)(52,111,56,107)(58,122,62,126)(60,128,64,124)(74,125,78,121)(76,123,80,127), (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), (1,29,18,55)(2,26,19,52)(3,31,20,49)(4,28,21,54)(5,25,22,51)(6,30,23,56)(7,27,24,53)(8,32,17,50)(9,90,43,83)(10,95,44,88)(11,92,45,85)(12,89,46,82)(13,94,47,87)(14,91,48,84)(15,96,41,81)(16,93,42,86)(33,109,124,119)(34,106,125,116)(35,111,126,113)(36,108,127,118)(37,105,128,115)(38,110,121,120)(39,107,122,117)(40,112,123,114)(57,71,76,104)(58,68,77,101)(59,65,78,98)(60,70,79,103)(61,67,80,100)(62,72,73,97)(63,69,74,102)(64,66,75,99) );
G=PermutationGroup([(1,24,5,20),(2,17,6,21),(3,18,7,22),(4,19,8,23),(9,41,13,45),(10,42,14,46),(11,43,15,47),(12,44,16,48),(25,49,29,53),(26,50,30,54),(27,51,31,55),(28,52,32,56),(33,122,37,126),(34,123,38,127),(35,124,39,128),(36,125,40,121),(57,74,61,78),(58,75,62,79),(59,76,63,80),(60,77,64,73),(65,104,69,100),(66,97,70,101),(67,98,71,102),(68,99,72,103),(81,94,85,90),(82,95,86,91),(83,96,87,92),(84,89,88,93),(105,113,109,117),(106,114,110,118),(107,115,111,119),(108,116,112,120)], [(1,61,18,80),(2,62,19,73),(3,63,20,74),(4,64,21,75),(5,57,22,76),(6,58,23,77),(7,59,24,78),(8,60,17,79),(9,118,43,108),(10,119,44,109),(11,120,45,110),(12,113,46,111),(13,114,47,112),(14,115,48,105),(15,116,41,106),(16,117,42,107),(25,104,51,71),(26,97,52,72),(27,98,53,65),(28,99,54,66),(29,100,55,67),(30,101,56,68),(31,102,49,69),(32,103,50,70),(33,95,124,88),(34,96,125,81),(35,89,126,82),(36,90,127,83),(37,91,128,84),(38,92,121,85),(39,93,122,86),(40,94,123,87)], [(1,90,5,94),(2,82,6,86),(3,96,7,92),(4,88,8,84),(9,71,13,67),(10,103,14,99),(11,69,15,65),(12,101,16,97),(17,91,21,95),(18,83,22,87),(19,89,23,93),(20,81,24,85),(25,112,29,108),(26,113,30,117),(27,110,31,106),(28,119,32,115),(33,79,37,75),(34,59,38,63),(35,77,39,73),(36,57,40,61),(41,98,45,102),(42,72,46,68),(43,104,47,100),(44,70,48,66),(49,116,53,120),(50,105,54,109),(51,114,55,118),(52,111,56,107),(58,122,62,126),(60,128,64,124),(74,125,78,121),(76,123,80,127)], [(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)], [(1,29,18,55),(2,26,19,52),(3,31,20,49),(4,28,21,54),(5,25,22,51),(6,30,23,56),(7,27,24,53),(8,32,17,50),(9,90,43,83),(10,95,44,88),(11,92,45,85),(12,89,46,82),(13,94,47,87),(14,91,48,84),(15,96,41,81),(16,93,42,86),(33,109,124,119),(34,106,125,116),(35,111,126,113),(36,108,127,118),(37,105,128,115),(38,110,121,120),(39,107,122,117),(40,112,123,114),(57,71,76,104),(58,68,77,101),(59,65,78,98),(60,70,79,103),(61,67,80,100),(62,72,73,97),(63,69,74,102),(64,66,75,99)])
Matrix representation of C42.255C23 ►in GL6(𝔽17)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 15 | 0 | 0 |
| 0 | 0 | 1 | 16 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 1 |
| 0 | 0 | 1 | 16 | 16 | 0 |
| 1 | 15 | 0 | 0 | 0 | 0 |
| 1 | 16 | 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 |
| 1 | 15 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 13 | 13 | 13 |
| 0 | 0 | 0 | 0 | 0 | 13 |
| 0 | 0 | 0 | 0 | 13 | 0 |
| 0 | 0 | 0 | 13 | 0 | 0 |
| 13 | 0 | 0 | 0 | 0 | 0 |
| 0 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 10 | 12 | 10 |
| 0 | 0 | 7 | 11 | 11 | 16 |
| 0 | 0 | 7 | 10 | 0 | 10 |
| 0 | 0 | 0 | 11 | 1 | 16 |
| 0 | 7 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 15 | 0 |
| 0 | 0 | 0 | 0 | 16 | 1 |
| 0 | 0 | 0 | 0 | 16 | 0 |
| 0 | 0 | 0 | 1 | 16 | 0 |
G:=sub<GL(6,GF(17))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,15,16,16,16,0,0,0,0,0,16,0,0,0,0,1,0],[1,1,0,0,0,0,15,16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,15,16,0,0,0,0,0,0,4,0,0,0,0,0,13,0,0,13,0,0,13,0,13,0,0,0,13,13,0,0],[13,0,0,0,0,0,0,13,0,0,0,0,0,0,7,7,7,0,0,0,10,11,10,11,0,0,12,11,0,1,0,0,10,16,10,16],[0,12,0,0,0,0,7,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,15,16,16,16,0,0,0,1,0,0] >;
C42.255C23 in GAP, Magma, Sage, TeX
C_4^2._{255}C_2^3 % in TeX
G:=Group("C4^2.255C2^3"); // GroupNames label
G:=SmallGroup(128,436);
// by ID
G=gap.SmallGroup(128,436);
# by ID
G:=PCGroup([7,-2,2,2,-2,2,-2,2,224,141,736,422,387,352,1123,136,2804,718,172]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=1,c^2=a^2,d^2=a^-1*b^2,e^2=b^2,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=a^-1*c,e*c*e^-1=b*c,e*d*e^-1=a^2*d>;
// generators/relations
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