direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C37⋊C4, C74⋊C4, D37⋊C4, D74.C2, D37.C22, C37⋊(C2×C4), SmallGroup(296,12)
Series: Derived ►Chief ►Lower central ►Upper central
| C37 — C2×C37⋊C4 |
Generators and relations for C2×C37⋊C4
G = < a,b,c | a2=b37=c4=1, ab=ba, ac=ca, cbc-1=b6 >
Character table of C2×C37⋊C4
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 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 | 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 | linear of order 2 |
| ρ5 | 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 |
| ρ6 | 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 |
| ρ7 | 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 |
| ρ8 | 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 |
| 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 | -ζ3735-ζ3725-ζ3712-ζ372 | -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 | orthogonal faithful |
| ρ10 | 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 | -ζ3736-ζ3731-ζ376-ζ37 | -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 | orthogonal faithful |
| ρ11 | 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 | -ζ3727-ζ3723-ζ3714-ζ3710 | -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 | orthogonal faithful |
| ρ12 | 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 | ζ3722+ζ3721+ζ3716+ζ3715 | 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 | orthogonal lifted from C37⋊C4 |
| ρ13 | 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 | ζ3732+ζ3730+ζ377+ζ375 | 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 | orthogonal lifted from C37⋊C4 |
| ρ14 | 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 | -ζ3734-ζ3719-ζ3718-ζ373 | -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 | orthogonal faithful |
| ρ15 | 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 | ζ3727+ζ3723+ζ3714+ζ3710 | 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 | orthogonal lifted from C37⋊C4 |
| ρ16 | 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 | ζ3733+ζ3724+ζ3713+ζ374 | 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 | orthogonal lifted from C37⋊C4 |
| ρ17 | 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 | -ζ3728-ζ3720-ζ3717-ζ379 | -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 | orthogonal faithful |
| ρ18 | 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 | ζ3728+ζ3720+ζ3717+ζ379 | 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 | orthogonal lifted from C37⋊C4 |
| ρ19 | 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 | ζ3734+ζ3719+ζ3718+ζ373 | 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 | orthogonal lifted from C37⋊C4 |
| ρ20 | 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 | -ζ3729-ζ3726-ζ3711-ζ378 | -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 | orthogonal faithful |
| 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 | ζ3729+ζ3726+ζ3711+ζ378 | 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 | orthogonal lifted from C37⋊C4 |
| ρ22 | 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 | -ζ3733-ζ3724-ζ3713-ζ374 | -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 | orthogonal faithful |
| ρ23 | 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 | ζ3736+ζ3731+ζ376+ζ37 | 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 | orthogonal lifted from C37⋊C4 |
| 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 | -ζ3722-ζ3721-ζ3716-ζ3715 | -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 | orthogonal faithful |
| 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 | -ζ3732-ζ3730-ζ377-ζ375 | -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 | orthogonal faithful |
| ρ26 | 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 | ζ3735+ζ3725+ζ3712+ζ372 | 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 | orthogonal lifted from C37⋊C4 |
►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)
(2 32 37 7)(3 26 36 13)(4 20 35 19)(5 14 34 25)(6 8 33 31)(9 27 30 12)(10 21 29 18)(11 15 28 24)(16 22 23 17)(39 69 74 44)(40 63 73 50)(41 57 72 56)(42 51 71 62)(43 45 70 68)(46 64 67 49)(47 58 66 55)(48 52 65 61)(53 59 60 54)
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), (2,32,37,7)(3,26,36,13)(4,20,35,19)(5,14,34,25)(6,8,33,31)(9,27,30,12)(10,21,29,18)(11,15,28,24)(16,22,23,17)(39,69,74,44)(40,63,73,50)(41,57,72,56)(42,51,71,62)(43,45,70,68)(46,64,67,49)(47,58,66,55)(48,52,65,61)(53,59,60,54)>;
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), (2,32,37,7)(3,26,36,13)(4,20,35,19)(5,14,34,25)(6,8,33,31)(9,27,30,12)(10,21,29,18)(11,15,28,24)(16,22,23,17)(39,69,74,44)(40,63,73,50)(41,57,72,56)(42,51,71,62)(43,45,70,68)(46,64,67,49)(47,58,66,55)(48,52,65,61)(53,59,60,54) );
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)], [(2,32,37,7),(3,26,36,13),(4,20,35,19),(5,14,34,25),(6,8,33,31),(9,27,30,12),(10,21,29,18),(11,15,28,24),(16,22,23,17),(39,69,74,44),(40,63,73,50),(41,57,72,56),(42,51,71,62),(43,45,70,68),(46,64,67,49),(47,58,66,55),(48,52,65,61),(53,59,60,54)]])
Matrix representation of C2×C37⋊C4 ►in GL4(𝔽149) generated by
| 148 | 0 | 0 | 0 |
| 0 | 148 | 0 | 0 |
| 0 | 0 | 148 | 0 |
| 0 | 0 | 0 | 148 |
| 134 | 3 | 134 | 148 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 70 | 22 | 14 | 96 |
| 73 | 71 | 136 | 56 |
| 64 | 70 | 87 | 139 |
G:=sub<GL(4,GF(149))| [148,0,0,0,0,148,0,0,0,0,148,0,0,0,0,148],[134,1,0,0,3,0,1,0,134,0,0,1,148,0,0,0],[1,70,73,64,0,22,71,70,0,14,136,87,0,96,56,139] >;
C2×C37⋊C4 in GAP, Magma, Sage, TeX
C_2\times C_{37}\rtimes C_4 % in TeX
G:=Group("C2xC37:C4"); // GroupNames label
G:=SmallGroup(296,12);
// by ID
G=gap.SmallGroup(296,12);
# by ID
G:=PCGroup([4,-2,-2,-2,-37,16,3971,1163]);
// Polycyclic
G:=Group<a,b,c|a^2=b^37=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^6>;
// generators/relations
Export
Subgroup lattice of C2×C37⋊C4 in TeX
Character table of C2×C37⋊C4 in TeX