metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C3⋊C8⋊3D4, C3⋊2(C8⋊D4), C4⋊C4.28D6, D6⋊3Q8⋊2C2, (C2×C8).177D6, C4.167(S3×D4), (C2×Q8).42D6, Q8⋊C4⋊18S3, C12⋊D4.3C2, C12.125(C2×D4), C2.D24⋊30C2, C6.Q16⋊10C2, C4.33(C4○D12), C12.20(C4○D4), C6.24(C4⋊D4), C2.18(Q8⋊3D6), C6.64(C8⋊C22), (C2×Dic3).33D4, (C22×S3).19D4, C22.202(S3×D4), (C6×Q8).35C22, C2.27(Dic3⋊D4), (C2×C24).244C22, (C2×C12).252C23, C2.16(Q16⋊S3), (C2×D12).66C22, C6.62(C8.C22), C4⋊Dic3.96C22, (C2×C8⋊S3)⋊20C2, (C2×Q8⋊2S3)⋊5C2, (C2×C6).265(C2×D4), (C2×C3⋊C8).43C22, (S3×C2×C4).25C22, (C3×Q8⋊C4)⋊27C2, (C3×C4⋊C4).53C22, (C2×C4).359(C22×S3), SmallGroup(192,371)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3⋊(C8⋊D4)
G = < a,b,c,d | a3=b8=c4=d2=1, bab-1=dad=a-1, ac=ca, cbc-1=b-1, dbd=b3, dcd=c-1 >
Subgroups: 408 in 120 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, S3, C6, C8, C2×C4, C2×C4, D4, Q8, C23, Dic3, C12, C12, D6, C2×C6, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), SD16, C22×C4, C2×D4, C2×Q8, C3⋊C8, C24, C4×S3, D12, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C3×Q8, C22×S3, C22×S3, D4⋊C4, Q8⋊C4, C2.D8, C4⋊D4, C22⋊Q8, C2×M4(2), C2×SD16, C8⋊S3, C2×C3⋊C8, Dic3⋊C4, C4⋊Dic3, D6⋊C4, Q8⋊2S3, C3×C4⋊C4, C2×C24, S3×C2×C4, C2×D12, C2×D12, C6×Q8, C8⋊D4, C6.Q16, C2.D24, C3×Q8⋊C4, C12⋊D4, C2×C8⋊S3, C2×Q8⋊2S3, D6⋊3Q8, C3⋊(C8⋊D4)
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, C22×S3, C4⋊D4, C8⋊C22, C8.C22, C4○D12, S3×D4, C8⋊D4, Dic3⋊D4, Q8⋊3D6, Q16⋊S3, C3⋊(C8⋊D4)
Character table of C3⋊(C8⋊D4)
| class | 1 | 2A | 2B | 2C | 2D | 2E | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 6A | 6B | 6C | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 12E | 12F | 24A | 24B | 24C | 24D | |
| size | 1 | 1 | 1 | 1 | 12 | 24 | 2 | 2 | 2 | 8 | 8 | 12 | 24 | 2 | 2 | 2 | 4 | 4 | 12 | 12 | 4 | 4 | 8 | 8 | 8 | 8 | 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 | 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 | 0 | -1 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ10 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | 2 | -2 | 0 | 0 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ11 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | -2 | -2 | 0 | 0 | -2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ12 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | -2 | 0 | 2 | -2 | -2 | 0 | 0 | 2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ15 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 0 | 0 | -2 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ16 | 2 | 2 | 2 | 2 | 0 | 0 | -1 | 2 | 2 | -2 | 2 | 0 | 0 | -1 | -1 | -1 | -2 | -2 | 0 | 0 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | orthogonal lifted from D6 |
| ρ17 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 2i | -2i | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | -2i | 2i | 2i | -2i | complex lifted from C4○D4 |
| ρ18 | 2 | 2 | -2 | -2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | -2i | 2i | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 2i | -2i | -2i | 2i | complex lifted from C4○D4 |
| ρ19 | 2 | 2 | -2 | -2 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | 2i | -2i | 0 | 0 | 1 | -1 | √-3 | -√3 | √3 | -√-3 | i | -i | -i | i | complex lifted from C4○D12 |
| ρ20 | 2 | 2 | -2 | -2 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | 2i | -2i | 0 | 0 | 1 | -1 | -√-3 | √3 | -√3 | √-3 | i | -i | -i | i | complex lifted from C4○D12 |
| ρ21 | 2 | 2 | -2 | -2 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -2i | 2i | 0 | 0 | 1 | -1 | -√-3 | -√3 | √3 | √-3 | -i | i | i | -i | complex lifted from C4○D12 |
| ρ22 | 2 | 2 | -2 | -2 | 0 | 0 | -1 | 2 | -2 | 0 | 0 | 0 | 0 | -1 | 1 | 1 | -2i | 2i | 0 | 0 | 1 | -1 | √-3 | √3 | -√3 | -√-3 | -i | i | i | -i | complex lifted from C4○D12 |
| ρ23 | 4 | -4 | 4 | -4 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | -4 | -4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C8⋊C22 |
| ρ24 | 4 | 4 | -4 | -4 | 0 | 0 | -2 | -4 | 4 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ25 | 4 | 4 | 4 | 4 | 0 | 0 | -2 | -4 | -4 | 0 | 0 | 0 | 0 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from S3×D4 |
| ρ26 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√6 | √6 | -√6 | √6 | orthogonal lifted from Q8⋊3D6 |
| ρ27 | 4 | -4 | 4 | -4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √6 | -√6 | √6 | -√6 | orthogonal lifted from Q8⋊3D6 |
| ρ28 | 4 | -4 | -4 | 4 | 0 | 0 | 4 | 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 |
| ρ29 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | √-6 | √-6 | -√-6 | -√-6 | complex lifted from Q16⋊S3 |
| ρ30 | 4 | -4 | -4 | 4 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -√-6 | -√-6 | √-6 | √-6 | complex lifted from Q16⋊S3 |
►On 96 points
Generators in S96
(1 38 66)(2 67 39)(3 40 68)(4 69 33)(5 34 70)(6 71 35)(7 36 72)(8 65 37)(9 58 82)(10 83 59)(11 60 84)(12 85 61)(13 62 86)(14 87 63)(15 64 88)(16 81 57)(17 25 54)(18 55 26)(19 27 56)(20 49 28)(21 29 50)(22 51 30)(23 31 52)(24 53 32)(41 91 74)(42 75 92)(43 93 76)(44 77 94)(45 95 78)(46 79 96)(47 89 80)(48 73 90)
(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)
(1 19 83 73)(2 18 84 80)(3 17 85 79)(4 24 86 78)(5 23 87 77)(6 22 88 76)(7 21 81 75)(8 20 82 74)(9 41 65 49)(10 48 66 56)(11 47 67 55)(12 46 68 54)(13 45 69 53)(14 44 70 52)(15 43 71 51)(16 42 72 50)(25 61 96 40)(26 60 89 39)(27 59 90 38)(28 58 91 37)(29 57 92 36)(30 64 93 35)(31 63 94 34)(32 62 95 33)
(1 83)(2 86)(3 81)(4 84)(5 87)(6 82)(7 85)(8 88)(9 35)(10 38)(11 33)(12 36)(13 39)(14 34)(15 37)(16 40)(17 21)(18 24)(20 22)(25 50)(26 53)(27 56)(28 51)(29 54)(30 49)(31 52)(32 55)(41 93)(42 96)(43 91)(44 94)(45 89)(46 92)(47 95)(48 90)(57 68)(58 71)(59 66)(60 69)(61 72)(62 67)(63 70)(64 65)(74 76)(75 79)(78 80)
G:=sub<Sym(96)| (1,38,66)(2,67,39)(3,40,68)(4,69,33)(5,34,70)(6,71,35)(7,36,72)(8,65,37)(9,58,82)(10,83,59)(11,60,84)(12,85,61)(13,62,86)(14,87,63)(15,64,88)(16,81,57)(17,25,54)(18,55,26)(19,27,56)(20,49,28)(21,29,50)(22,51,30)(23,31,52)(24,53,32)(41,91,74)(42,75,92)(43,93,76)(44,77,94)(45,95,78)(46,79,96)(47,89,80)(48,73,90), (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), (1,19,83,73)(2,18,84,80)(3,17,85,79)(4,24,86,78)(5,23,87,77)(6,22,88,76)(7,21,81,75)(8,20,82,74)(9,41,65,49)(10,48,66,56)(11,47,67,55)(12,46,68,54)(13,45,69,53)(14,44,70,52)(15,43,71,51)(16,42,72,50)(25,61,96,40)(26,60,89,39)(27,59,90,38)(28,58,91,37)(29,57,92,36)(30,64,93,35)(31,63,94,34)(32,62,95,33), (1,83)(2,86)(3,81)(4,84)(5,87)(6,82)(7,85)(8,88)(9,35)(10,38)(11,33)(12,36)(13,39)(14,34)(15,37)(16,40)(17,21)(18,24)(20,22)(25,50)(26,53)(27,56)(28,51)(29,54)(30,49)(31,52)(32,55)(41,93)(42,96)(43,91)(44,94)(45,89)(46,92)(47,95)(48,90)(57,68)(58,71)(59,66)(60,69)(61,72)(62,67)(63,70)(64,65)(74,76)(75,79)(78,80)>;
G:=Group( (1,38,66)(2,67,39)(3,40,68)(4,69,33)(5,34,70)(6,71,35)(7,36,72)(8,65,37)(9,58,82)(10,83,59)(11,60,84)(12,85,61)(13,62,86)(14,87,63)(15,64,88)(16,81,57)(17,25,54)(18,55,26)(19,27,56)(20,49,28)(21,29,50)(22,51,30)(23,31,52)(24,53,32)(41,91,74)(42,75,92)(43,93,76)(44,77,94)(45,95,78)(46,79,96)(47,89,80)(48,73,90), (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), (1,19,83,73)(2,18,84,80)(3,17,85,79)(4,24,86,78)(5,23,87,77)(6,22,88,76)(7,21,81,75)(8,20,82,74)(9,41,65,49)(10,48,66,56)(11,47,67,55)(12,46,68,54)(13,45,69,53)(14,44,70,52)(15,43,71,51)(16,42,72,50)(25,61,96,40)(26,60,89,39)(27,59,90,38)(28,58,91,37)(29,57,92,36)(30,64,93,35)(31,63,94,34)(32,62,95,33), (1,83)(2,86)(3,81)(4,84)(5,87)(6,82)(7,85)(8,88)(9,35)(10,38)(11,33)(12,36)(13,39)(14,34)(15,37)(16,40)(17,21)(18,24)(20,22)(25,50)(26,53)(27,56)(28,51)(29,54)(30,49)(31,52)(32,55)(41,93)(42,96)(43,91)(44,94)(45,89)(46,92)(47,95)(48,90)(57,68)(58,71)(59,66)(60,69)(61,72)(62,67)(63,70)(64,65)(74,76)(75,79)(78,80) );
G=PermutationGroup([[(1,38,66),(2,67,39),(3,40,68),(4,69,33),(5,34,70),(6,71,35),(7,36,72),(8,65,37),(9,58,82),(10,83,59),(11,60,84),(12,85,61),(13,62,86),(14,87,63),(15,64,88),(16,81,57),(17,25,54),(18,55,26),(19,27,56),(20,49,28),(21,29,50),(22,51,30),(23,31,52),(24,53,32),(41,91,74),(42,75,92),(43,93,76),(44,77,94),(45,95,78),(46,79,96),(47,89,80),(48,73,90)], [(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)], [(1,19,83,73),(2,18,84,80),(3,17,85,79),(4,24,86,78),(5,23,87,77),(6,22,88,76),(7,21,81,75),(8,20,82,74),(9,41,65,49),(10,48,66,56),(11,47,67,55),(12,46,68,54),(13,45,69,53),(14,44,70,52),(15,43,71,51),(16,42,72,50),(25,61,96,40),(26,60,89,39),(27,59,90,38),(28,58,91,37),(29,57,92,36),(30,64,93,35),(31,63,94,34),(32,62,95,33)], [(1,83),(2,86),(3,81),(4,84),(5,87),(6,82),(7,85),(8,88),(9,35),(10,38),(11,33),(12,36),(13,39),(14,34),(15,37),(16,40),(17,21),(18,24),(20,22),(25,50),(26,53),(27,56),(28,51),(29,54),(30,49),(31,52),(32,55),(41,93),(42,96),(43,91),(44,94),(45,89),(46,92),(47,95),(48,90),(57,68),(58,71),(59,66),(60,69),(61,72),(62,67),(63,70),(64,65),(74,76),(75,79),(78,80)]])
Matrix representation of C3⋊(C8⋊D4) ►in GL6(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 1 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 0 | 0 | 72 | 72 | 72 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 3 | 5 | 7 |
| 0 | 0 | 72 | 6 | 7 | 2 |
| 0 | 0 | 50 | 44 | 68 | 0 |
| 0 | 0 | 48 | 49 | 0 | 71 |
| 45 | 2 | 0 | 0 | 0 | 0 |
| 9 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 55 | 13 | 60 |
| 0 | 0 | 31 | 4 | 26 | 13 |
| 0 | 0 | 0 | 18 | 69 | 18 |
| 0 | 0 | 42 | 0 | 42 | 64 |
| 72 | 0 | 0 | 0 | 0 | 0 |
| 45 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 72 | 0 | 0 |
| 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 1 | 0 |
| 0 | 0 | 24 | 24 | 72 | 72 |
G:=sub<GL(6,GF(73))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,72,72,1,0,0,0,1,0,0,72,0,0,0,0,0,72,0,0,0,0,1,72],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,72,50,48,0,0,3,6,44,49,0,0,5,7,68,0,0,0,7,2,0,71],[45,9,0,0,0,0,2,28,0,0,0,0,0,0,9,31,0,42,0,0,55,4,18,0,0,0,13,26,69,42,0,0,60,13,18,64],[72,45,0,0,0,0,0,1,0,0,0,0,0,0,0,72,25,24,0,0,72,0,25,24,0,0,0,0,1,72,0,0,0,0,0,72] >;
C3⋊(C8⋊D4) in GAP, Magma, Sage, TeX
C_3\rtimes (C_8\rtimes D_4)
% in TeX
G:=Group("C3:(C8:D4)"); // GroupNames label
G:=SmallGroup(192,371);
// by ID
G=gap.SmallGroup(192,371);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,253,120,1094,135,184,570,297,136,6278]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^8=c^4=d^2=1,b*a*b^-1=d*a*d=a^-1,a*c=c*a,c*b*c^-1=b^-1,d*b*d=b^3,d*c*d=c^-1>;
// generators/relations
Export