G = C6.GL2(𝔽3) order 288 = 25·32
3rd non-split extension by C6 of GL2(𝔽3) acting via GL2(𝔽3)/SL2(𝔽3)=C2
Aliases: C6.3GL2(𝔽3), C6.3CSU2(𝔽3), SL2(𝔽3)⋊1Dic3, C3⋊(Q8⋊Dic3), Q8⋊(C3⋊Dic3), (C2×C6).12S4, (C6×Q8).5S3, C6.6(A4⋊C4), C2.(C6.5S4), C2.(C6.6S4), (C3×Q8)⋊1Dic3, C22.3(C3⋊S4), C2.2(C6.7S4), (C3×SL2(𝔽3))⋊1C4, (C2×SL2(𝔽3)).1S3, (C6×SL2(𝔽3)).1C2, (C2×Q8).1(C3⋊S3), SmallGroup(288,403)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C2 — Q8 — C3×SL2(𝔽3) — C6.GL2(𝔽3) |
| C1 — C2 — Q8 — C3×Q8 — C3×SL2(𝔽3) — C6×SL2(𝔽3) — C6.GL2(𝔽3) |
| C3×SL2(𝔽3) — C6.GL2(𝔽3) |
Generators and relations for C6.GL2(𝔽3)
G = < a,b,c,d,e | a6=b4=d3=1, c2=b2, e2=a3, ab=ba, ac=ca, ad=da, eae-1=a-1, cbc-1=ece-1=b-1, dbd-1=bc, ebe-1=b2c, dcd-1=b, ede-1=d-1 >
Subgroups: 388 in 78 conjugacy classes, 23 normal (17 characteristic)
C1, C2, C3, C3, C4, C22, C6, C6, C8, C2×C4, Q8, Q8, C32, Dic3, C12, C2×C6, C2×C6, C4⋊C4, C2×C8, C2×Q8, C3×C6, C3⋊C8, SL2(𝔽3), C2×Dic3, C2×C12, C3×Q8, C3×Q8, Q8⋊C4, C3⋊Dic3, C62, C2×C3⋊C8, C4⋊Dic3, C2×SL2(𝔽3), C6×Q8, C3×SL2(𝔽3), C2×C3⋊Dic3, Q8⋊2Dic3, Q8⋊Dic3, C6×SL2(𝔽3), C6.GL2(𝔽3)
Quotients: C1, C2, C4, S3, Dic3, C3⋊S3, S4, C3⋊Dic3, CSU2(𝔽3), GL2(𝔽3), A4⋊C4, C3⋊S4, Q8⋊Dic3, C6.5S4, C6.6S4, C6.7S4, C6.GL2(𝔽3)
Character table of C6.GL2(𝔽3)
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 4D | 6A | 6B | 6C | 6D | 6E | 6F | 6G | 6H | 6I | 6J | 6K | 6L | 8A | 8B | 8C | 8D | 12A | 12B | |
| size | 1 | 1 | 1 | 1 | 2 | 8 | 8 | 8 | 6 | 6 | 36 | 36 | 2 | 2 | 2 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 18 | 18 | 18 | 18 | 12 | 12 | |
| 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 | i | -i | -1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | i | -i | -i | i | -1 | 1 | linear of order 4 |
| ρ4 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -i | i | -1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | -i | i | i | -i | -1 | 1 | linear of order 4 |
| ρ5 | 2 | 2 | 2 | 2 | -1 | -1 | 2 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | 2 | 0 | 0 | 0 | 0 | -1 | -1 | orthogonal lifted from S3 |
| ρ6 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | 2 | -1 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | orthogonal lifted from S3 |
| ρ7 | 2 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 2 | 2 | orthogonal lifted from S3 |
| ρ8 | 2 | 2 | 2 | 2 | -1 | 2 | -1 | -1 | 2 | 2 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | -1 | -1 | 2 | -1 | 0 | 0 | 0 | 0 | -1 | -1 | orthogonal lifted from S3 |
| ρ9 | 2 | 2 | -2 | -2 | 2 | -1 | -1 | -1 | 2 | -2 | 0 | 0 | -2 | 2 | -2 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | -2 | 2 | symplectic lifted from Dic3, Schur index 2 |
| ρ10 | 2 | 2 | -2 | -2 | -1 | -1 | 2 | -1 | 2 | -2 | 0 | 0 | 1 | -1 | 1 | -1 | -2 | -2 | 1 | 1 | 1 | 1 | -1 | 2 | 0 | 0 | 0 | 0 | 1 | -1 | symplectic lifted from Dic3, Schur index 2 |
| ρ11 | 2 | 2 | -2 | -2 | -1 | -1 | -1 | 2 | 2 | -2 | 0 | 0 | 1 | -1 | 1 | 2 | 1 | 1 | 1 | 1 | -2 | -2 | -1 | -1 | 0 | 0 | 0 | 0 | 1 | -1 | symplectic lifted from Dic3, Schur index 2 |
| ρ12 | 2 | 2 | -2 | -2 | -1 | 2 | -1 | -1 | 2 | -2 | 0 | 0 | 1 | -1 | 1 | -1 | 1 | 1 | -2 | -2 | 1 | 1 | 2 | -1 | 0 | 0 | 0 | 0 | 1 | -1 | symplectic lifted from Dic3, Schur index 2 |
| ρ13 | 2 | -2 | 2 | -2 | 2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | √2 | √2 | -√2 | -√2 | 0 | 0 | symplectic lifted from CSU2(𝔽3), Schur index 2 |
| ρ14 | 2 | -2 | 2 | -2 | 2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | -2 | -2 | 2 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -√2 | -√2 | √2 | √2 | 0 | 0 | symplectic lifted from CSU2(𝔽3), Schur index 2 |
| ρ15 | 2 | -2 | -2 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | √-2 | -√-2 | √-2 | -√-2 | 0 | 0 | complex lifted from GL2(𝔽3) |
| ρ16 | 2 | -2 | -2 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 2 | -2 | -2 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | -√-2 | √-2 | -√-2 | √-2 | 0 | 0 | complex lifted from GL2(𝔽3) |
| ρ17 | 3 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | -1 | -1 | orthogonal lifted from S4 |
| ρ18 | 3 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | -1 | -1 | 1 | 1 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S4 |
| ρ19 | 3 | 3 | -3 | -3 | 3 | 0 | 0 | 0 | -1 | 1 | -i | i | -3 | 3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | i | -i | -i | i | 1 | -1 | complex lifted from A4⋊C4 |
| ρ20 | 3 | 3 | -3 | -3 | 3 | 0 | 0 | 0 | -1 | 1 | i | -i | -3 | 3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -i | i | i | -i | 1 | -1 | complex lifted from A4⋊C4 |
| ρ21 | 4 | -4 | -4 | 4 | -2 | 1 | 1 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | 2 | 1 | -1 | 1 | -1 | -2 | 2 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C6.6S4 |
| ρ22 | 4 | -4 | -4 | 4 | -2 | 1 | -2 | 1 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -1 | -2 | 2 | 1 | -1 | 1 | -1 | -1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C6.6S4 |
| ρ23 | 4 | -4 | -4 | 4 | 4 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 4 | -4 | -4 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from GL2(𝔽3) |
| ρ24 | 4 | -4 | -4 | 4 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | -2 | 2 | 2 | -1 | 1 | -1 | -2 | 2 | 1 | -1 | 2 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | orthogonal lifted from C6.6S4 |
| ρ25 | 4 | -4 | 4 | -4 | -2 | -2 | 1 | 1 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -1 | -1 | 1 | 2 | -2 | -1 | 1 | 2 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C6.5S4, Schur index 2 |
| ρ26 | 4 | -4 | 4 | -4 | -2 | 1 | 1 | -2 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 2 | -1 | 1 | -1 | 1 | 2 | -2 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C6.5S4, Schur index 2 |
| ρ27 | 4 | -4 | 4 | -4 | 4 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | -4 | -4 | 4 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from CSU2(𝔽3), Schur index 2 |
| ρ28 | 4 | -4 | 4 | -4 | -2 | 1 | -2 | 1 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -1 | 2 | -2 | -1 | 1 | -1 | 1 | -1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C6.5S4, Schur index 2 |
| ρ29 | 6 | 6 | 6 | 6 | -3 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | -3 | -3 | -3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | orthogonal lifted from C3⋊S4 |
| ρ30 | 6 | 6 | -6 | -6 | -3 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 3 | -3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | 1 | symplectic lifted from C6.7S4, Schur index 2 |
►On 96 points
Generators in S96
(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 77 57 49)(2 78 58 50)(3 73 59 51)(4 74 60 52)(5 75 55 53)(6 76 56 54)(7 89 66 17)(8 90 61 18)(9 85 62 13)(10 86 63 14)(11 87 64 15)(12 88 65 16)(19 81 71 45)(20 82 72 46)(21 83 67 47)(22 84 68 48)(23 79 69 43)(24 80 70 44)(25 92 37 31)(26 93 38 32)(27 94 39 33)(28 95 40 34)(29 96 41 35)(30 91 42 36)
(1 19 57 71)(2 20 58 72)(3 21 59 67)(4 22 60 68)(5 23 55 69)(6 24 56 70)(7 37 66 25)(8 38 61 26)(9 39 62 27)(10 40 63 28)(11 41 64 29)(12 42 65 30)(13 33 85 94)(14 34 86 95)(15 35 87 96)(16 36 88 91)(17 31 89 92)(18 32 90 93)(43 53 79 75)(44 54 80 76)(45 49 81 77)(46 50 82 78)(47 51 83 73)(48 52 84 74)
(13 27 33)(14 28 34)(15 29 35)(16 30 36)(17 25 31)(18 26 32)(19 45 77)(20 46 78)(21 47 73)(22 48 74)(23 43 75)(24 44 76)(37 92 89)(38 93 90)(39 94 85)(40 95 86)(41 96 87)(42 91 88)(49 71 81)(50 72 82)(51 67 83)(52 68 84)(53 69 79)(54 70 80)
(1 64 4 61)(2 63 5 66)(3 62 6 65)(7 58 10 55)(8 57 11 60)(9 56 12 59)(13 70 16 67)(14 69 17 72)(15 68 18 71)(19 87 22 90)(20 86 23 89)(21 85 24 88)(25 50 28 53)(26 49 29 52)(27 54 30 51)(31 82 34 79)(32 81 35 84)(33 80 36 83)(37 78 40 75)(38 77 41 74)(39 76 42 73)(43 92 46 95)(44 91 47 94)(45 96 48 93)
G:=sub<Sym(96)| (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), (1,77,57,49)(2,78,58,50)(3,73,59,51)(4,74,60,52)(5,75,55,53)(6,76,56,54)(7,89,66,17)(8,90,61,18)(9,85,62,13)(10,86,63,14)(11,87,64,15)(12,88,65,16)(19,81,71,45)(20,82,72,46)(21,83,67,47)(22,84,68,48)(23,79,69,43)(24,80,70,44)(25,92,37,31)(26,93,38,32)(27,94,39,33)(28,95,40,34)(29,96,41,35)(30,91,42,36), (1,19,57,71)(2,20,58,72)(3,21,59,67)(4,22,60,68)(5,23,55,69)(6,24,56,70)(7,37,66,25)(8,38,61,26)(9,39,62,27)(10,40,63,28)(11,41,64,29)(12,42,65,30)(13,33,85,94)(14,34,86,95)(15,35,87,96)(16,36,88,91)(17,31,89,92)(18,32,90,93)(43,53,79,75)(44,54,80,76)(45,49,81,77)(46,50,82,78)(47,51,83,73)(48,52,84,74), (13,27,33)(14,28,34)(15,29,35)(16,30,36)(17,25,31)(18,26,32)(19,45,77)(20,46,78)(21,47,73)(22,48,74)(23,43,75)(24,44,76)(37,92,89)(38,93,90)(39,94,85)(40,95,86)(41,96,87)(42,91,88)(49,71,81)(50,72,82)(51,67,83)(52,68,84)(53,69,79)(54,70,80), (1,64,4,61)(2,63,5,66)(3,62,6,65)(7,58,10,55)(8,57,11,60)(9,56,12,59)(13,70,16,67)(14,69,17,72)(15,68,18,71)(19,87,22,90)(20,86,23,89)(21,85,24,88)(25,50,28,53)(26,49,29,52)(27,54,30,51)(31,82,34,79)(32,81,35,84)(33,80,36,83)(37,78,40,75)(38,77,41,74)(39,76,42,73)(43,92,46,95)(44,91,47,94)(45,96,48,93)>;
G:=Group( (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), (1,77,57,49)(2,78,58,50)(3,73,59,51)(4,74,60,52)(5,75,55,53)(6,76,56,54)(7,89,66,17)(8,90,61,18)(9,85,62,13)(10,86,63,14)(11,87,64,15)(12,88,65,16)(19,81,71,45)(20,82,72,46)(21,83,67,47)(22,84,68,48)(23,79,69,43)(24,80,70,44)(25,92,37,31)(26,93,38,32)(27,94,39,33)(28,95,40,34)(29,96,41,35)(30,91,42,36), (1,19,57,71)(2,20,58,72)(3,21,59,67)(4,22,60,68)(5,23,55,69)(6,24,56,70)(7,37,66,25)(8,38,61,26)(9,39,62,27)(10,40,63,28)(11,41,64,29)(12,42,65,30)(13,33,85,94)(14,34,86,95)(15,35,87,96)(16,36,88,91)(17,31,89,92)(18,32,90,93)(43,53,79,75)(44,54,80,76)(45,49,81,77)(46,50,82,78)(47,51,83,73)(48,52,84,74), (13,27,33)(14,28,34)(15,29,35)(16,30,36)(17,25,31)(18,26,32)(19,45,77)(20,46,78)(21,47,73)(22,48,74)(23,43,75)(24,44,76)(37,92,89)(38,93,90)(39,94,85)(40,95,86)(41,96,87)(42,91,88)(49,71,81)(50,72,82)(51,67,83)(52,68,84)(53,69,79)(54,70,80), (1,64,4,61)(2,63,5,66)(3,62,6,65)(7,58,10,55)(8,57,11,60)(9,56,12,59)(13,70,16,67)(14,69,17,72)(15,68,18,71)(19,87,22,90)(20,86,23,89)(21,85,24,88)(25,50,28,53)(26,49,29,52)(27,54,30,51)(31,82,34,79)(32,81,35,84)(33,80,36,83)(37,78,40,75)(38,77,41,74)(39,76,42,73)(43,92,46,95)(44,91,47,94)(45,96,48,93) );
G=PermutationGroup([[(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)], [(1,77,57,49),(2,78,58,50),(3,73,59,51),(4,74,60,52),(5,75,55,53),(6,76,56,54),(7,89,66,17),(8,90,61,18),(9,85,62,13),(10,86,63,14),(11,87,64,15),(12,88,65,16),(19,81,71,45),(20,82,72,46),(21,83,67,47),(22,84,68,48),(23,79,69,43),(24,80,70,44),(25,92,37,31),(26,93,38,32),(27,94,39,33),(28,95,40,34),(29,96,41,35),(30,91,42,36)], [(1,19,57,71),(2,20,58,72),(3,21,59,67),(4,22,60,68),(5,23,55,69),(6,24,56,70),(7,37,66,25),(8,38,61,26),(9,39,62,27),(10,40,63,28),(11,41,64,29),(12,42,65,30),(13,33,85,94),(14,34,86,95),(15,35,87,96),(16,36,88,91),(17,31,89,92),(18,32,90,93),(43,53,79,75),(44,54,80,76),(45,49,81,77),(46,50,82,78),(47,51,83,73),(48,52,84,74)], [(13,27,33),(14,28,34),(15,29,35),(16,30,36),(17,25,31),(18,26,32),(19,45,77),(20,46,78),(21,47,73),(22,48,74),(23,43,75),(24,44,76),(37,92,89),(38,93,90),(39,94,85),(40,95,86),(41,96,87),(42,91,88),(49,71,81),(50,72,82),(51,67,83),(52,68,84),(53,69,79),(54,70,80)], [(1,64,4,61),(2,63,5,66),(3,62,6,65),(7,58,10,55),(8,57,11,60),(9,56,12,59),(13,70,16,67),(14,69,17,72),(15,68,18,71),(19,87,22,90),(20,86,23,89),(21,85,24,88),(25,50,28,53),(26,49,29,52),(27,54,30,51),(31,82,34,79),(32,81,35,84),(33,80,36,83),(37,78,40,75),(38,77,41,74),(39,76,42,73),(43,92,46,95),(44,91,47,94),(45,96,48,93)]])
Matrix representation of C6.GL2(𝔽3) ►in GL4(𝔽73) generated by
| 0 | 72 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 72 | 0 |
| 0 | 0 | 0 | 72 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 60 | 48 |
| 0 | 0 | 36 | 13 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 38 | 59 |
| 0 | 0 | 25 | 35 |
| 72 | 72 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 24 | 35 |
| 0 | 0 | 60 | 48 |
| 27 | 0 | 0 | 0 |
| 46 | 46 | 0 | 0 |
| 0 | 0 | 60 | 43 |
| 0 | 0 | 30 | 13 |
G:=sub<GL(4,GF(73))| [0,1,0,0,72,1,0,0,0,0,72,0,0,0,0,72],[1,0,0,0,0,1,0,0,0,0,60,36,0,0,48,13],[1,0,0,0,0,1,0,0,0,0,38,25,0,0,59,35],[72,1,0,0,72,0,0,0,0,0,24,60,0,0,35,48],[27,46,0,0,0,46,0,0,0,0,60,30,0,0,43,13] >;
C6.GL2(𝔽3) in GAP, Magma, Sage, TeX
C_6.{\rm GL}_2({\mathbb F}_3) % in TeX
G:=Group("C6.GL(2,3)"); // GroupNames label
G:=SmallGroup(288,403);
// by ID
G=gap.SmallGroup(288,403);
# by ID
G:=PCGroup([7,-2,-2,-3,-3,-2,2,-2,14,170,675,2524,1908,172,1517,1153,285,124]);
// Polycyclic
G:=Group<a,b,c,d,e|a^6=b^4=d^3=1,c^2=b^2,e^2=a^3,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1,c*b*c^-1=e*c*e^-1=b^-1,d*b*d^-1=b*c,e*b*e^-1=b^2*c,d*c*d^-1=b,e*d*e^-1=d^-1>;
// generators/relations
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