metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C37⋊C8, C74.C4, Dic37.2C2, C2.(C37⋊C4), SmallGroup(296,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C37 — C37⋊C8 |
Generators and relations for C37⋊C8
G = < a,b | a37=b8=1, bab-1=a6 >
Character table of C37⋊C8
| class | 1 | 2 | 4A | 4B | 8A | 8B | 8C | 8D | 37A | 37B | 37C | 37D | 37E | 37F | 37G | 37H | 37I | 74A | 74B | 74C | 74D | 74E | 74F | 74G | 74H | 74I | |
| size | 1 | 1 | 37 | 37 | 37 | 37 | 37 | 37 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 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 | 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 | linear of order 2 |
| ρ3 | 1 | 1 | -1 | -1 | -i | i | -i | i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ4 | 1 | 1 | -1 | -1 | i | -i | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ5 | 1 | -1 | i | -i | ζ83 | ζ8 | ζ87 | ζ85 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ6 | 1 | -1 | -i | i | ζ85 | ζ87 | ζ8 | ζ83 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ7 | 1 | -1 | -i | i | ζ8 | ζ83 | ζ85 | ζ87 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ8 | 1 | -1 | i | -i | ζ87 | ζ85 | ζ83 | ζ8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 8 |
| ρ9 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3736+ζ3731+ζ376+ζ37 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3732+ζ3730+ζ377+ζ375 | ζ3732+ζ3730+ζ377+ζ375 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3736+ζ3731+ζ376+ζ37 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | orthogonal lifted from C37⋊C4 |
| ρ10 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | orthogonal lifted from C37⋊C4 |
| ρ11 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3736+ζ3731+ζ376+ζ37 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3736+ζ3731+ζ376+ζ37 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | orthogonal lifted from C37⋊C4 |
| ρ12 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | orthogonal lifted from C37⋊C4 |
| ρ13 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3732+ζ3730+ζ377+ζ375 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3732+ζ3730+ζ377+ζ375 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | orthogonal lifted from C37⋊C4 |
| ρ14 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3736+ζ3731+ζ376+ζ37 | ζ3736+ζ3731+ζ376+ζ37 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | orthogonal lifted from C37⋊C4 |
| ρ15 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | orthogonal lifted from C37⋊C4 |
| ρ16 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | orthogonal lifted from C37⋊C4 |
| ρ17 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3732+ζ3730+ζ377+ζ375 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3732+ζ3730+ζ377+ζ375 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | orthogonal lifted from C37⋊C4 |
| ρ18 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3732+ζ3730+ζ377+ζ375 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3735+ζ3725+ζ3712+ζ372 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3727-ζ3723-ζ3714-ζ3710 | symplectic faithful, Schur index 2 |
| ρ19 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3722+ζ3721+ζ3716+ζ3715 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3736-ζ3731-ζ376-ζ37 | symplectic faithful, Schur index 2 |
| ρ20 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3736+ζ3731+ζ376+ζ37 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3732+ζ3730+ζ377+ζ375 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3735-ζ3725-ζ3712-ζ372 | symplectic faithful, Schur index 2 |
| ρ21 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3736+ζ3731+ζ376+ζ37 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3728+ζ3720+ζ3717+ζ379 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3729-ζ3726-ζ3711-ζ378 | symplectic faithful, Schur index 2 |
| ρ22 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3733+ζ3724+ζ3713+ζ374 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3728-ζ3720-ζ3717-ζ379 | symplectic faithful, Schur index 2 |
| ρ23 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3732+ζ3730+ζ377+ζ375 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3736+ζ3731+ζ376+ζ37 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3727+ζ3723+ζ3714+ζ3710 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3733-ζ3724-ζ3713-ζ374 | symplectic faithful, Schur index 2 |
| ρ24 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3734+ζ3719+ζ3718+ζ373 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3722-ζ3721-ζ3716-ζ3715 | symplectic faithful, Schur index 2 |
| ρ25 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3729+ζ3726+ζ3711+ζ378 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3732+ζ3730+ζ377+ζ375 | ζ3736+ζ3731+ζ376+ζ37 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3734-ζ3719-ζ3718-ζ373 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3732-ζ3730-ζ377-ζ375 | symplectic faithful, Schur index 2 |
| ρ26 | 4 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | ζ3733+ζ3724+ζ3713+ζ374 | ζ3736+ζ3731+ζ376+ζ37 | ζ3732+ζ3730+ζ377+ζ375 | ζ3727+ζ3723+ζ3714+ζ3710 | ζ3722+ζ3721+ζ3716+ζ3715 | ζ3728+ζ3720+ζ3717+ζ379 | ζ3735+ζ3725+ζ3712+ζ372 | ζ3734+ζ3719+ζ3718+ζ373 | ζ3729+ζ3726+ζ3711+ζ378 | -ζ3729-ζ3726-ζ3711-ζ378 | -ζ3733-ζ3724-ζ3713-ζ374 | -ζ3736-ζ3731-ζ376-ζ37 | -ζ3732-ζ3730-ζ377-ζ375 | -ζ3727-ζ3723-ζ3714-ζ3710 | -ζ3722-ζ3721-ζ3716-ζ3715 | -ζ3728-ζ3720-ζ3717-ζ379 | -ζ3735-ζ3725-ζ3712-ζ372 | -ζ3734-ζ3719-ζ3718-ζ373 | symplectic faithful, Schur index 2 |
►Regular action on 296 points
Generators in S296
(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)(112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148)(149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185)(186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222)(223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259)(260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296)
(1 288 112 193 45 233 75 164)(2 282 148 199 46 227 111 170)(3 276 147 205 47 258 110 176)(4 270 146 211 48 252 109 182)(5 264 145 217 49 246 108 151)(6 295 144 186 50 240 107 157)(7 289 143 192 51 234 106 163)(8 283 142 198 52 228 105 169)(9 277 141 204 53 259 104 175)(10 271 140 210 54 253 103 181)(11 265 139 216 55 247 102 150)(12 296 138 222 56 241 101 156)(13 290 137 191 57 235 100 162)(14 284 136 197 58 229 99 168)(15 278 135 203 59 223 98 174)(16 272 134 209 60 254 97 180)(17 266 133 215 61 248 96 149)(18 260 132 221 62 242 95 155)(19 291 131 190 63 236 94 161)(20 285 130 196 64 230 93 167)(21 279 129 202 65 224 92 173)(22 273 128 208 66 255 91 179)(23 267 127 214 67 249 90 185)(24 261 126 220 68 243 89 154)(25 292 125 189 69 237 88 160)(26 286 124 195 70 231 87 166)(27 280 123 201 71 225 86 172)(28 274 122 207 72 256 85 178)(29 268 121 213 73 250 84 184)(30 262 120 219 74 244 83 153)(31 293 119 188 38 238 82 159)(32 287 118 194 39 232 81 165)(33 281 117 200 40 226 80 171)(34 275 116 206 41 257 79 177)(35 269 115 212 42 251 78 183)(36 263 114 218 43 245 77 152)(37 294 113 187 44 239 76 158)
G:=sub<Sym(296)| (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)(112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148)(149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185)(186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222)(223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259)(260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296), (1,288,112,193,45,233,75,164)(2,282,148,199,46,227,111,170)(3,276,147,205,47,258,110,176)(4,270,146,211,48,252,109,182)(5,264,145,217,49,246,108,151)(6,295,144,186,50,240,107,157)(7,289,143,192,51,234,106,163)(8,283,142,198,52,228,105,169)(9,277,141,204,53,259,104,175)(10,271,140,210,54,253,103,181)(11,265,139,216,55,247,102,150)(12,296,138,222,56,241,101,156)(13,290,137,191,57,235,100,162)(14,284,136,197,58,229,99,168)(15,278,135,203,59,223,98,174)(16,272,134,209,60,254,97,180)(17,266,133,215,61,248,96,149)(18,260,132,221,62,242,95,155)(19,291,131,190,63,236,94,161)(20,285,130,196,64,230,93,167)(21,279,129,202,65,224,92,173)(22,273,128,208,66,255,91,179)(23,267,127,214,67,249,90,185)(24,261,126,220,68,243,89,154)(25,292,125,189,69,237,88,160)(26,286,124,195,70,231,87,166)(27,280,123,201,71,225,86,172)(28,274,122,207,72,256,85,178)(29,268,121,213,73,250,84,184)(30,262,120,219,74,244,83,153)(31,293,119,188,38,238,82,159)(32,287,118,194,39,232,81,165)(33,281,117,200,40,226,80,171)(34,275,116,206,41,257,79,177)(35,269,115,212,42,251,78,183)(36,263,114,218,43,245,77,152)(37,294,113,187,44,239,76,158)>;
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)(75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111)(112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148)(149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185)(186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222)(223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259)(260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296), (1,288,112,193,45,233,75,164)(2,282,148,199,46,227,111,170)(3,276,147,205,47,258,110,176)(4,270,146,211,48,252,109,182)(5,264,145,217,49,246,108,151)(6,295,144,186,50,240,107,157)(7,289,143,192,51,234,106,163)(8,283,142,198,52,228,105,169)(9,277,141,204,53,259,104,175)(10,271,140,210,54,253,103,181)(11,265,139,216,55,247,102,150)(12,296,138,222,56,241,101,156)(13,290,137,191,57,235,100,162)(14,284,136,197,58,229,99,168)(15,278,135,203,59,223,98,174)(16,272,134,209,60,254,97,180)(17,266,133,215,61,248,96,149)(18,260,132,221,62,242,95,155)(19,291,131,190,63,236,94,161)(20,285,130,196,64,230,93,167)(21,279,129,202,65,224,92,173)(22,273,128,208,66,255,91,179)(23,267,127,214,67,249,90,185)(24,261,126,220,68,243,89,154)(25,292,125,189,69,237,88,160)(26,286,124,195,70,231,87,166)(27,280,123,201,71,225,86,172)(28,274,122,207,72,256,85,178)(29,268,121,213,73,250,84,184)(30,262,120,219,74,244,83,153)(31,293,119,188,38,238,82,159)(32,287,118,194,39,232,81,165)(33,281,117,200,40,226,80,171)(34,275,116,206,41,257,79,177)(35,269,115,212,42,251,78,183)(36,263,114,218,43,245,77,152)(37,294,113,187,44,239,76,158) );
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),(75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111),(112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148),(149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185),(186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222),(223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259),(260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296)], [(1,288,112,193,45,233,75,164),(2,282,148,199,46,227,111,170),(3,276,147,205,47,258,110,176),(4,270,146,211,48,252,109,182),(5,264,145,217,49,246,108,151),(6,295,144,186,50,240,107,157),(7,289,143,192,51,234,106,163),(8,283,142,198,52,228,105,169),(9,277,141,204,53,259,104,175),(10,271,140,210,54,253,103,181),(11,265,139,216,55,247,102,150),(12,296,138,222,56,241,101,156),(13,290,137,191,57,235,100,162),(14,284,136,197,58,229,99,168),(15,278,135,203,59,223,98,174),(16,272,134,209,60,254,97,180),(17,266,133,215,61,248,96,149),(18,260,132,221,62,242,95,155),(19,291,131,190,63,236,94,161),(20,285,130,196,64,230,93,167),(21,279,129,202,65,224,92,173),(22,273,128,208,66,255,91,179),(23,267,127,214,67,249,90,185),(24,261,126,220,68,243,89,154),(25,292,125,189,69,237,88,160),(26,286,124,195,70,231,87,166),(27,280,123,201,71,225,86,172),(28,274,122,207,72,256,85,178),(29,268,121,213,73,250,84,184),(30,262,120,219,74,244,83,153),(31,293,119,188,38,238,82,159),(32,287,118,194,39,232,81,165),(33,281,117,200,40,226,80,171),(34,275,116,206,41,257,79,177),(35,269,115,212,42,251,78,183),(36,263,114,218,43,245,77,152),(37,294,113,187,44,239,76,158)]])
Matrix representation of C37⋊C8 ►in GL4(𝔽593) generated by
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 592 | 570 | 157 | 570 |
| 111 | 207 | 135 | 562 |
| 475 | 382 | 118 | 390 |
| 490 | 120 | 37 | 388 |
| 386 | 78 | 468 | 63 |
G:=sub<GL(4,GF(593))| [0,0,0,592,1,0,0,570,0,1,0,157,0,0,1,570],[111,475,490,386,207,382,120,78,135,118,37,468,562,390,388,63] >;
C37⋊C8 in GAP, Magma, Sage, TeX
C_{37}\rtimes C_8 % in TeX
G:=Group("C37:C8"); // GroupNames label
G:=SmallGroup(296,3);
// by ID
G=gap.SmallGroup(296,3);
# by ID
G:=PCGroup([4,-2,-2,-2,-37,8,21,3971,2311]);
// Polycyclic
G:=Group<a,b|a^37=b^8=1,b*a*b^-1=a^6>;
// generators/relations
Export
Subgroup lattice of C37⋊C8 in TeX
Character table of C37⋊C8 in TeX