metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.65D6, C3⋊C8.7D4, C4.13(S3×D4), (C2×D4).50D6, (C2×C12).83D4, C12.27(C2×D4), C3⋊2(C8.2D4), (C2×Q8).64D6, C12⋊2Q8⋊18C2, C4.4D4.7S3, C6.19(C4⋊1D4), (C6×D4).66C22, (C6×Q8).58C22, C2.10(C12⋊3D4), (C4×C12).109C22, (C2×C12).378C23, C42.S3⋊10C2, C2.19(Q8.14D6), C6.120(C8.C22), (C2×Dic6).108C22, (C2×C3⋊Q16)⋊14C2, (C2×C6).509(C2×D4), (C2×D4.S3).7C2, (C2×C4).63(C3⋊D4), (C2×C3⋊C8).123C22, (C3×C4.4D4).5C2, (C2×C4).478(C22×S3), C22.184(C2×C3⋊D4), SmallGroup(192,619)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.65D6
G = < a,b,c,d | a4=b4=c6=1, d2=b, ab=ba, cac-1=a-1b2, dad-1=ab2, cbc-1=b-1, bd=db, dcd-1=b-1c-1 >
Subgroups: 336 in 124 conjugacy classes, 43 normal (19 characteristic)
C1, C2, C2, C2, C3, C4, C4, C22, C22, C6, C6, C6, C8, C2×C4, C2×C4, C2×C4, D4, Q8, C23, Dic3, C12, C12, C2×C6, C2×C6, C42, C22⋊C4, C4⋊C4, C2×C8, SD16, Q16, C2×D4, C2×Q8, C2×Q8, C3⋊C8, Dic6, C2×Dic3, C2×C12, C2×C12, C2×C12, C3×D4, C3×Q8, C22×C6, C8⋊C4, C4.4D4, C4⋊Q8, C2×SD16, C2×Q16, C2×C3⋊C8, C4⋊Dic3, D4.S3, C3⋊Q16, C4×C12, C3×C22⋊C4, C2×Dic6, C6×D4, C6×Q8, C8.2D4, C42.S3, C12⋊2Q8, C2×D4.S3, C2×C3⋊Q16, C3×C4.4D4, C42.65D6
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C3⋊D4, C22×S3, C4⋊1D4, C8.C22, S3×D4, C2×C3⋊D4, C8.2D4, C12⋊3D4, Q8.14D6, C42.65D6
Character table of C42.65D6
| class | 1 | 2A | 2B | 2C | 2D | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 6A | 6B | 6C | 6D | 6E | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | 12G | 12H | |
| size | 1 | 1 | 1 | 1 | 8 | 2 | 2 | 2 | 4 | 4 | 8 | 24 | 24 | 2 | 2 | 2 | 8 | 8 | 12 | 12 | 12 | 12 | 4 | 4 | 4 | 4 | 4 | 4 | 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 | 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 | 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 | -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 | -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 | -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 | -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 | 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 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | linear of order 2 |
| ρ9 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | 2 | -2 | 0 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ10 | 2 | -2 | -2 | 2 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | -2 | 0 | 2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | -2 | -1 | 2 | 2 | 2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | orthogonal lifted from D6 |
| ρ12 | 2 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ13 | 2 | -2 | -2 | 2 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | -2 | 0 | 2 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | -2 | -1 | 2 | 2 | -2 | -2 | 2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | orthogonal lifted from D6 |
| ρ15 | 2 | -2 | -2 | 2 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ16 | 2 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | -2 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ17 | 2 | -2 | -2 | 2 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | -2 | 0 | 0 | 0 | 2 | 0 | -2 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ18 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | 0 | orthogonal lifted from D4 |
| ρ19 | 2 | 2 | 2 | 2 | 0 | -1 | -2 | -2 | 2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | √-3 | -√-3 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 1 | 1 | 1 | -√-3 | √-3 | complex lifted from C3⋊D4 |
| ρ20 | 2 | 2 | 2 | 2 | 0 | -1 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | √-3 | -√-3 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | √-3 | -√-3 | complex lifted from C3⋊D4 |
| ρ21 | 2 | 2 | 2 | 2 | 0 | -1 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | -1 | -1 | -1 | -√-3 | √-3 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | -√-3 | √-3 | complex lifted from C3⋊D4 |
| ρ22 | 2 | 2 | 2 | 2 | 0 | -1 | -2 | -2 | 2 | -2 | 0 | 0 | 0 | -1 | -1 | -1 | -√-3 | √-3 | 0 | 0 | 0 | 0 | 1 | -1 | -1 | 1 | 1 | 1 | √-3 | -√-3 | complex lifted from C3⋊D4 |
| ρ23 | 4 | -4 | -4 | 4 | 0 | -2 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ24 | 4 | -4 | -4 | 4 | 0 | -2 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ25 | 4 | -4 | 4 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | -4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ26 | 4 | 4 | -4 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ27 | 4 | 4 | -4 | -4 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√3 | -2√3 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8.14D6, Schur index 2 |
| ρ28 | 4 | 4 | -4 | -4 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√3 | 2√3 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from Q8.14D6, Schur index 2 |
| ρ29 | 4 | -4 | 4 | -4 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2√3 | -2√3 | 0 | 0 | symplectic lifted from Q8.14D6, Schur index 2 |
| ρ30 | 4 | -4 | 4 | -4 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2√3 | 2√3 | 0 | 0 | symplectic lifted from Q8.14D6, Schur index 2 |
►On 96 points
Generators in S96
(1 21 42 13)(2 18 43 10)(3 23 44 15)(4 20 45 12)(5 17 46 9)(6 22 47 14)(7 19 48 11)(8 24 41 16)(25 52 57 88)(26 49 58 85)(27 54 59 82)(28 51 60 87)(29 56 61 84)(30 53 62 81)(31 50 63 86)(32 55 64 83)(33 89 70 77)(34 94 71 74)(35 91 72 79)(36 96 65 76)(37 93 66 73)(38 90 67 78)(39 95 68 75)(40 92 69 80)
(1 3 5 7)(2 4 6 8)(9 11 13 15)(10 12 14 16)(17 19 21 23)(18 20 22 24)(25 27 29 31)(26 28 30 32)(33 35 37 39)(34 36 38 40)(41 43 45 47)(42 44 46 48)(49 51 53 55)(50 52 54 56)(57 59 61 63)(58 60 62 64)(65 67 69 71)(66 68 70 72)(73 75 77 79)(74 76 78 80)(81 83 85 87)(82 84 86 88)(89 91 93 95)(90 92 94 96)
(1 84 91)(2 94 85 4 92 87)(3 82 93 7 86 89)(5 88 95)(6 90 81 8 96 83)(9 29 39 21 57 72)(10 67 58 24 40 32)(11 27 33 19 59 70)(12 65 60 22 34 30)(13 25 35 17 61 68)(14 71 62 20 36 28)(15 31 37 23 63 66)(16 69 64 18 38 26)(41 76 55 47 78 53)(42 56 79)(43 74 49 45 80 51)(44 54 73 48 50 77)(46 52 75)
(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)
G:=sub<Sym(96)| (1,21,42,13)(2,18,43,10)(3,23,44,15)(4,20,45,12)(5,17,46,9)(6,22,47,14)(7,19,48,11)(8,24,41,16)(25,52,57,88)(26,49,58,85)(27,54,59,82)(28,51,60,87)(29,56,61,84)(30,53,62,81)(31,50,63,86)(32,55,64,83)(33,89,70,77)(34,94,71,74)(35,91,72,79)(36,96,65,76)(37,93,66,73)(38,90,67,78)(39,95,68,75)(40,92,69,80), (1,3,5,7)(2,4,6,8)(9,11,13,15)(10,12,14,16)(17,19,21,23)(18,20,22,24)(25,27,29,31)(26,28,30,32)(33,35,37,39)(34,36,38,40)(41,43,45,47)(42,44,46,48)(49,51,53,55)(50,52,54,56)(57,59,61,63)(58,60,62,64)(65,67,69,71)(66,68,70,72)(73,75,77,79)(74,76,78,80)(81,83,85,87)(82,84,86,88)(89,91,93,95)(90,92,94,96), (1,84,91)(2,94,85,4,92,87)(3,82,93,7,86,89)(5,88,95)(6,90,81,8,96,83)(9,29,39,21,57,72)(10,67,58,24,40,32)(11,27,33,19,59,70)(12,65,60,22,34,30)(13,25,35,17,61,68)(14,71,62,20,36,28)(15,31,37,23,63,66)(16,69,64,18,38,26)(41,76,55,47,78,53)(42,56,79)(43,74,49,45,80,51)(44,54,73,48,50,77)(46,52,75), (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)>;
G:=Group( (1,21,42,13)(2,18,43,10)(3,23,44,15)(4,20,45,12)(5,17,46,9)(6,22,47,14)(7,19,48,11)(8,24,41,16)(25,52,57,88)(26,49,58,85)(27,54,59,82)(28,51,60,87)(29,56,61,84)(30,53,62,81)(31,50,63,86)(32,55,64,83)(33,89,70,77)(34,94,71,74)(35,91,72,79)(36,96,65,76)(37,93,66,73)(38,90,67,78)(39,95,68,75)(40,92,69,80), (1,3,5,7)(2,4,6,8)(9,11,13,15)(10,12,14,16)(17,19,21,23)(18,20,22,24)(25,27,29,31)(26,28,30,32)(33,35,37,39)(34,36,38,40)(41,43,45,47)(42,44,46,48)(49,51,53,55)(50,52,54,56)(57,59,61,63)(58,60,62,64)(65,67,69,71)(66,68,70,72)(73,75,77,79)(74,76,78,80)(81,83,85,87)(82,84,86,88)(89,91,93,95)(90,92,94,96), (1,84,91)(2,94,85,4,92,87)(3,82,93,7,86,89)(5,88,95)(6,90,81,8,96,83)(9,29,39,21,57,72)(10,67,58,24,40,32)(11,27,33,19,59,70)(12,65,60,22,34,30)(13,25,35,17,61,68)(14,71,62,20,36,28)(15,31,37,23,63,66)(16,69,64,18,38,26)(41,76,55,47,78,53)(42,56,79)(43,74,49,45,80,51)(44,54,73,48,50,77)(46,52,75), (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) );
G=PermutationGroup([[(1,21,42,13),(2,18,43,10),(3,23,44,15),(4,20,45,12),(5,17,46,9),(6,22,47,14),(7,19,48,11),(8,24,41,16),(25,52,57,88),(26,49,58,85),(27,54,59,82),(28,51,60,87),(29,56,61,84),(30,53,62,81),(31,50,63,86),(32,55,64,83),(33,89,70,77),(34,94,71,74),(35,91,72,79),(36,96,65,76),(37,93,66,73),(38,90,67,78),(39,95,68,75),(40,92,69,80)], [(1,3,5,7),(2,4,6,8),(9,11,13,15),(10,12,14,16),(17,19,21,23),(18,20,22,24),(25,27,29,31),(26,28,30,32),(33,35,37,39),(34,36,38,40),(41,43,45,47),(42,44,46,48),(49,51,53,55),(50,52,54,56),(57,59,61,63),(58,60,62,64),(65,67,69,71),(66,68,70,72),(73,75,77,79),(74,76,78,80),(81,83,85,87),(82,84,86,88),(89,91,93,95),(90,92,94,96)], [(1,84,91),(2,94,85,4,92,87),(3,82,93,7,86,89),(5,88,95),(6,90,81,8,96,83),(9,29,39,21,57,72),(10,67,58,24,40,32),(11,27,33,19,59,70),(12,65,60,22,34,30),(13,25,35,17,61,68),(14,71,62,20,36,28),(15,31,37,23,63,66),(16,69,64,18,38,26),(41,76,55,47,78,53),(42,56,79),(43,74,49,45,80,51),(44,54,73,48,50,77),(46,52,75)], [(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)]])
Matrix representation of C42.65D6 ►in GL8(𝔽73)
| 15 | 28 | 69 | 0 | 0 | 0 | 0 | 0 |
| 45 | 60 | 0 | 69 | 0 | 0 | 0 | 0 |
| 43 | 14 | 58 | 45 | 0 | 0 | 0 | 0 |
| 59 | 29 | 28 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 66 | 59 |
| 0 | 0 | 0 | 0 | 0 | 0 | 14 | 7 |
| 0 | 0 | 0 | 0 | 7 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 59 | 66 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 72 | 0 | 0 |
| 72 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 43 | 29 | 1 | 1 | 0 | 0 | 0 | 0 |
| 44 | 14 | 72 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 72 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
| 42 | 45 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 31 | 0 | 0 | 0 | 0 | 0 | 0 |
| 44 | 19 | 42 | 45 | 0 | 0 | 0 | 0 |
| 48 | 29 | 3 | 31 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 69 | 28 | 4 | 45 |
| 0 | 0 | 0 | 0 | 32 | 4 | 41 | 69 |
| 0 | 0 | 0 | 0 | 69 | 28 | 69 | 28 |
| 0 | 0 | 0 | 0 | 32 | 4 | 32 | 4 |
G:=sub<GL(8,GF(73))| [15,45,43,59,0,0,0,0,28,60,14,29,0,0,0,0,69,0,58,28,0,0,0,0,0,69,45,13,0,0,0,0,0,0,0,0,0,0,7,59,0,0,0,0,0,0,14,66,0,0,0,0,66,14,0,0,0,0,0,0,59,7,0,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[72,1,43,44,0,0,0,0,72,0,29,14,0,0,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,72,1,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,1,0],[42,3,44,48,0,0,0,0,45,31,19,29,0,0,0,0,0,0,42,3,0,0,0,0,0,0,45,31,0,0,0,0,0,0,0,0,69,32,69,32,0,0,0,0,28,4,28,4,0,0,0,0,4,41,69,32,0,0,0,0,45,69,28,4] >;
C42.65D6 in GAP, Magma, Sage, TeX
C_4^2._{65}D_6 % in TeX
G:=Group("C4^2.65D6"); // GroupNames label
G:=SmallGroup(192,619);
// by ID
G=gap.SmallGroup(192,619);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,253,120,254,555,1123,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^6=1,d^2=b,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations
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