direct product, metacyclic, supersoluble, monomial, A-group
Aliases: C2×C37⋊C6, C74⋊C6, D74⋊C3, D37⋊C6, C37⋊(C2×C6), C37⋊C3⋊C22, (C2×C37⋊C3)⋊C2, SmallGroup(444,8)
Series: Derived ►Chief ►Lower central ►Upper central
| C37 — C2×C37⋊C6 |
Generators and relations for C2×C37⋊C6
G = < a,b,c | a2=b37=c6=1, ab=ba, ac=ca, cbc-1=b11 >
Character table of C2×C37⋊C6
| class | 1 | 2A | 2B | 2C | 3A | 3B | 6A | 6B | 6C | 6D | 6E | 6F | 37A | 37B | 37C | 37D | 37E | 37F | 74A | 74B | 74C | 74D | 74E | 74F | |
| size | 1 | 1 | 37 | 37 | 37 | 37 | 37 | 37 | 37 | 37 | 37 | 37 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | |
| 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 | 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 | 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 | 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 | linear of order 2 |
| ρ5 | 1 | 1 | -1 | -1 | ζ32 | ζ3 | ζ6 | ζ65 | ζ6 | ζ32 | ζ65 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ6 | 1 | 1 | 1 | 1 | ζ32 | ζ3 | ζ32 | ζ3 | ζ32 | ζ32 | ζ3 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ7 | 1 | -1 | -1 | 1 | ζ3 | ζ32 | ζ3 | ζ6 | ζ65 | ζ65 | ζ32 | ζ6 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ8 | 1 | 1 | -1 | -1 | ζ3 | ζ32 | ζ65 | ζ6 | ζ65 | ζ3 | ζ6 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 6 |
| ρ9 | 1 | -1 | 1 | -1 | ζ3 | ζ32 | ζ65 | ζ32 | ζ3 | ζ65 | ζ6 | ζ6 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ10 | 1 | 1 | 1 | 1 | ζ3 | ζ32 | ζ3 | ζ32 | ζ3 | ζ3 | ζ32 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ11 | 1 | -1 | -1 | 1 | ζ32 | ζ3 | ζ32 | ζ65 | ζ6 | ζ6 | ζ3 | ζ65 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ12 | 1 | -1 | 1 | -1 | ζ32 | ζ3 | ζ6 | ζ3 | ζ32 | ζ6 | ζ65 | ζ65 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ13 | 6 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | -ζ3735-ζ3722-ζ3720-ζ3717-ζ3715-ζ372 | -ζ3728-ζ3725-ζ3721-ζ3716-ζ3712-ζ379 | -ζ3734-ζ3733-ζ3730-ζ377-ζ374-ζ373 | -ζ3731-ζ3729-ζ3723-ζ3714-ζ378-ζ376 | -ζ3732-ζ3724-ζ3719-ζ3718-ζ3713-ζ375 | -ζ3736-ζ3727-ζ3726-ζ3711-ζ3710-ζ37 | orthogonal faithful |
| ρ14 | 6 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | -ζ3728-ζ3725-ζ3721-ζ3716-ζ3712-ζ379 | -ζ3735-ζ3722-ζ3720-ζ3717-ζ3715-ζ372 | -ζ3732-ζ3724-ζ3719-ζ3718-ζ3713-ζ375 | -ζ3736-ζ3727-ζ3726-ζ3711-ζ3710-ζ37 | -ζ3734-ζ3733-ζ3730-ζ377-ζ374-ζ373 | -ζ3731-ζ3729-ζ3723-ζ3714-ζ378-ζ376 | orthogonal faithful |
| ρ15 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | orthogonal lifted from C37⋊C6 |
| ρ16 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | orthogonal lifted from C37⋊C6 |
| ρ17 | 6 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | -ζ3734-ζ3733-ζ3730-ζ377-ζ374-ζ373 | -ζ3732-ζ3724-ζ3719-ζ3718-ζ3713-ζ375 | -ζ3731-ζ3729-ζ3723-ζ3714-ζ378-ζ376 | -ζ3728-ζ3725-ζ3721-ζ3716-ζ3712-ζ379 | -ζ3736-ζ3727-ζ3726-ζ3711-ζ3710-ζ37 | -ζ3735-ζ3722-ζ3720-ζ3717-ζ3715-ζ372 | orthogonal faithful |
| ρ18 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | orthogonal lifted from C37⋊C6 |
| ρ19 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | orthogonal lifted from C37⋊C6 |
| ρ20 | 6 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | -ζ3731-ζ3729-ζ3723-ζ3714-ζ378-ζ376 | -ζ3736-ζ3727-ζ3726-ζ3711-ζ3710-ζ37 | -ζ3728-ζ3725-ζ3721-ζ3716-ζ3712-ζ379 | -ζ3732-ζ3724-ζ3719-ζ3718-ζ3713-ζ375 | -ζ3735-ζ3722-ζ3720-ζ3717-ζ3715-ζ372 | -ζ3734-ζ3733-ζ3730-ζ377-ζ374-ζ373 | orthogonal faithful |
| ρ21 | 6 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | -ζ3736-ζ3727-ζ3726-ζ3711-ζ3710-ζ37 | -ζ3731-ζ3729-ζ3723-ζ3714-ζ378-ζ376 | -ζ3735-ζ3722-ζ3720-ζ3717-ζ3715-ζ372 | -ζ3734-ζ3733-ζ3730-ζ377-ζ374-ζ373 | -ζ3728-ζ3725-ζ3721-ζ3716-ζ3712-ζ379 | -ζ3732-ζ3724-ζ3719-ζ3718-ζ3713-ζ375 | orthogonal faithful |
| ρ22 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | orthogonal lifted from C37⋊C6 |
| ρ23 | 6 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | orthogonal lifted from C37⋊C6 |
| ρ24 | 6 | -6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3732+ζ3724+ζ3719+ζ3718+ζ3713+ζ375 | ζ3734+ζ3733+ζ3730+ζ377+ζ374+ζ373 | ζ3736+ζ3727+ζ3726+ζ3711+ζ3710+ζ37 | ζ3735+ζ3722+ζ3720+ζ3717+ζ3715+ζ372 | ζ3731+ζ3729+ζ3723+ζ3714+ζ378+ζ376 | ζ3728+ζ3725+ζ3721+ζ3716+ζ3712+ζ379 | -ζ3732-ζ3724-ζ3719-ζ3718-ζ3713-ζ375 | -ζ3734-ζ3733-ζ3730-ζ377-ζ374-ζ373 | -ζ3736-ζ3727-ζ3726-ζ3711-ζ3710-ζ37 | -ζ3735-ζ3722-ζ3720-ζ3717-ζ3715-ζ372 | -ζ3731-ζ3729-ζ3723-ζ3714-ζ378-ζ376 | -ζ3728-ζ3725-ζ3721-ζ3716-ζ3712-ζ379 | orthogonal faithful |
►On 74 points
Generators in S74
(1 38)(2 39)(3 40)(4 41)(5 42)(6 43)(7 44)(8 45)(9 46)(10 47)(11 48)(12 49)(13 50)(14 51)(15 52)(16 53)(17 54)(18 55)(19 56)(20 57)(21 58)(22 59)(23 60)(24 61)(25 62)(26 63)(27 64)(28 65)(29 66)(30 67)(31 68)(32 69)(33 70)(34 71)(35 72)(36 73)(37 74)
(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)
(1 38)(2 65 27 74 11 49)(3 55 16 73 21 60)(4 45 5 72 31 71)(6 62 20 70 14 56)(7 52 9 69 24 67)(8 42 35 68 34 41)(10 59 13 66 17 63)(12 39 28 64 37 48)(15 46 32 61 30 44)(18 53 36 58 23 40)(19 43 25 57 33 51)(22 50 29 54 26 47)
G:=sub<Sym(74)| (1,38)(2,39)(3,40)(4,41)(5,42)(6,43)(7,44)(8,45)(9,46)(10,47)(11,48)(12,49)(13,50)(14,51)(15,52)(16,53)(17,54)(18,55)(19,56)(20,57)(21,58)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74), (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), (1,38)(2,65,27,74,11,49)(3,55,16,73,21,60)(4,45,5,72,31,71)(6,62,20,70,14,56)(7,52,9,69,24,67)(8,42,35,68,34,41)(10,59,13,66,17,63)(12,39,28,64,37,48)(15,46,32,61,30,44)(18,53,36,58,23,40)(19,43,25,57,33,51)(22,50,29,54,26,47)>;
G:=Group( (1,38)(2,39)(3,40)(4,41)(5,42)(6,43)(7,44)(8,45)(9,46)(10,47)(11,48)(12,49)(13,50)(14,51)(15,52)(16,53)(17,54)(18,55)(19,56)(20,57)(21,58)(22,59)(23,60)(24,61)(25,62)(26,63)(27,64)(28,65)(29,66)(30,67)(31,68)(32,69)(33,70)(34,71)(35,72)(36,73)(37,74), (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), (1,38)(2,65,27,74,11,49)(3,55,16,73,21,60)(4,45,5,72,31,71)(6,62,20,70,14,56)(7,52,9,69,24,67)(8,42,35,68,34,41)(10,59,13,66,17,63)(12,39,28,64,37,48)(15,46,32,61,30,44)(18,53,36,58,23,40)(19,43,25,57,33,51)(22,50,29,54,26,47) );
G=PermutationGroup([[(1,38),(2,39),(3,40),(4,41),(5,42),(6,43),(7,44),(8,45),(9,46),(10,47),(11,48),(12,49),(13,50),(14,51),(15,52),(16,53),(17,54),(18,55),(19,56),(20,57),(21,58),(22,59),(23,60),(24,61),(25,62),(26,63),(27,64),(28,65),(29,66),(30,67),(31,68),(32,69),(33,70),(34,71),(35,72),(36,73),(37,74)], [(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)], [(1,38),(2,65,27,74,11,49),(3,55,16,73,21,60),(4,45,5,72,31,71),(6,62,20,70,14,56),(7,52,9,69,24,67),(8,42,35,68,34,41),(10,59,13,66,17,63),(12,39,28,64,37,48),(15,46,32,61,30,44),(18,53,36,58,23,40),(19,43,25,57,33,51),(22,50,29,54,26,47)]])
Matrix representation of C2×C37⋊C6 ►in GL6(𝔽223)
| 222 | 0 | 0 | 0 | 0 | 0 |
| 0 | 222 | 0 | 0 | 0 | 0 |
| 0 | 0 | 222 | 0 | 0 | 0 |
| 0 | 0 | 0 | 222 | 0 | 0 |
| 0 | 0 | 0 | 0 | 222 | 0 |
| 0 | 0 | 0 | 0 | 0 | 222 |
| 37 | 147 | 93 | 126 | 42 | 222 |
| 166 | 89 | 29 | 140 | 121 | 98 |
| 5 | 51 | 109 | 11 | 78 | 30 |
| 195 | 166 | 15 | 206 | 143 | 55 |
| 177 | 209 | 23 | 212 | 219 | 170 |
| 62 | 174 | 192 | 181 | 210 | 149 |
| 33 | 66 | 184 | 156 | 129 | 78 |
| 164 | 4 | 59 | 142 | 139 | 31 |
| 196 | 193 | 32 | 173 | 54 | 108 |
| 65 | 150 | 69 | 102 | 212 | 77 |
| 146 | 56 | 141 | 16 | 204 | 182 |
| 82 | 111 | 52 | 124 | 187 | 71 |
G:=sub<GL(6,GF(223))| [222,0,0,0,0,0,0,222,0,0,0,0,0,0,222,0,0,0,0,0,0,222,0,0,0,0,0,0,222,0,0,0,0,0,0,222],[37,166,5,195,177,62,147,89,51,166,209,174,93,29,109,15,23,192,126,140,11,206,212,181,42,121,78,143,219,210,222,98,30,55,170,149],[33,164,196,65,146,82,66,4,193,150,56,111,184,59,32,69,141,52,156,142,173,102,16,124,129,139,54,212,204,187,78,31,108,77,182,71] >;
C2×C37⋊C6 in GAP, Magma, Sage, TeX
C_2\times C_{37}\rtimes C_6 % in TeX
G:=Group("C2xC37:C6"); // GroupNames label
G:=SmallGroup(444,8);
// by ID
G=gap.SmallGroup(444,8);
# by ID
G:=PCGroup([4,-2,-2,-3,-37,6915,1259]);
// Polycyclic
G:=Group<a,b,c|a^2=b^37=c^6=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^11>;
// generators/relations
Export
Subgroup lattice of C2×C37⋊C6 in TeX
Character table of C2×C37⋊C6 in TeX