metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C73⋊C4, D73.C2, SmallGroup(292,3)
Series: Derived ►Chief ►Lower central ►Upper central
C73 — C73⋊C4 |
Generators and relations for C73⋊C4
G = < a,b | a73=b4=1, bab-1=a46 >
Character table of C73⋊C4
class | 1 | 2 | 4A | 4B | 73A | 73B | 73C | 73D | 73E | 73F | 73G | 73H | 73I | 73J | 73K | 73L | 73M | 73N | 73O | 73P | 73Q | 73R | |
size | 1 | 73 | 73 | 73 | 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 | trivial |
ρ2 | 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 | 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 | -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 | 4 | 0 | 0 | 0 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7370+ζ7365+ζ738+ζ733 | orthogonal faithful |
ρ6 | 4 | 0 | 0 | 0 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7370+ζ7365+ζ738+ζ733 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7372+ζ7346+ζ7327+ζ73 | orthogonal faithful |
ρ7 | 4 | 0 | 0 | 0 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7370+ζ7365+ζ738+ζ733 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7342+ζ7339+ζ7334+ζ7331 | orthogonal faithful |
ρ8 | 4 | 0 | 0 | 0 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7370+ζ7365+ζ738+ζ733 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7369+ζ7338+ζ7335+ζ734 | orthogonal faithful |
ρ9 | 4 | 0 | 0 | 0 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7370+ζ7365+ζ738+ζ733 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7347+ζ7345+ζ7328+ζ7326 | orthogonal faithful |
ρ10 | 4 | 0 | 0 | 0 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7370+ζ7365+ζ738+ζ733 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7353+ζ7344+ζ7329+ζ7320 | orthogonal faithful |
ρ11 | 4 | 0 | 0 | 0 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7370+ζ7365+ζ738+ζ733 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7358+ζ7340+ζ7333+ζ7315 | orthogonal faithful |
ρ12 | 4 | 0 | 0 | 0 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7370+ζ7365+ζ738+ζ733 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7356+ζ7352+ζ7321+ζ7317 | orthogonal faithful |
ρ13 | 4 | 0 | 0 | 0 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7370+ζ7365+ζ738+ζ733 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7364+ζ7349+ζ7324+ζ739 | orthogonal faithful |
ρ14 | 4 | 0 | 0 | 0 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7370+ζ7365+ζ738+ζ733 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7350+ζ7337+ζ7336+ζ7323 | orthogonal faithful |
ρ15 | 4 | 0 | 0 | 0 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7370+ζ7365+ζ738+ζ733 | ζ7361+ζ7341+ζ7332+ζ7312 | orthogonal faithful |
ρ16 | 4 | 0 | 0 | 0 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7370+ζ7365+ζ738+ζ733 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7371+ζ7354+ζ7319+ζ732 | orthogonal faithful |
ρ17 | 4 | 0 | 0 | 0 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7370+ζ7365+ζ738+ζ733 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7368+ζ7362+ζ7311+ζ735 | orthogonal faithful |
ρ18 | 4 | 0 | 0 | 0 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7370+ζ7365+ζ738+ζ733 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7360+ζ7359+ζ7314+ζ7313 | orthogonal faithful |
ρ19 | 4 | 0 | 0 | 0 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7370+ζ7365+ζ738+ζ733 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7366+ζ7343+ζ7330+ζ737 | orthogonal faithful |
ρ20 | 4 | 0 | 0 | 0 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7370+ζ7365+ζ738+ζ733 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7355+ζ7348+ζ7325+ζ7318 | orthogonal faithful |
ρ21 | 4 | 0 | 0 | 0 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7370+ζ7365+ζ738+ζ733 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7367+ζ7357+ζ7316+ζ736 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7363+ζ7351+ζ7322+ζ7310 | orthogonal faithful |
ρ22 | 4 | 0 | 0 | 0 | ζ7370+ζ7365+ζ738+ζ733 | ζ7363+ζ7351+ζ7322+ζ7310 | ζ7361+ζ7341+ζ7332+ζ7312 | ζ7360+ζ7359+ζ7314+ζ7313 | ζ7355+ζ7348+ζ7325+ζ7318 | ζ7353+ζ7344+ζ7329+ζ7320 | ζ7364+ζ7349+ζ7324+ζ739 | ζ7347+ζ7345+ζ7328+ζ7326 | ζ7366+ζ7343+ζ7330+ζ737 | ζ7342+ζ7339+ζ7334+ζ7331 | ζ7350+ζ7337+ζ7336+ζ7323 | ζ7358+ζ7340+ζ7333+ζ7315 | ζ7372+ζ7346+ζ7327+ζ73 | ζ7356+ζ7352+ζ7321+ζ7317 | ζ7368+ζ7362+ζ7311+ζ735 | ζ7371+ζ7354+ζ7319+ζ732 | ζ7369+ζ7338+ζ7335+ζ734 | ζ7367+ζ7357+ζ7316+ζ736 | orthogonal faithful |
(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)
(2 28 73 47)(3 55 72 20)(4 9 71 66)(5 36 70 39)(6 63 69 12)(7 17 68 58)(8 44 67 31)(10 25 65 50)(11 52 64 23)(13 33 62 42)(14 60 61 15)(16 41 59 34)(18 22 57 53)(19 49 56 26)(21 30 54 45)(24 38 51 37)(27 46 48 29)(32 35 43 40)
G:=sub<Sym(73)| (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), (2,28,73,47)(3,55,72,20)(4,9,71,66)(5,36,70,39)(6,63,69,12)(7,17,68,58)(8,44,67,31)(10,25,65,50)(11,52,64,23)(13,33,62,42)(14,60,61,15)(16,41,59,34)(18,22,57,53)(19,49,56,26)(21,30,54,45)(24,38,51,37)(27,46,48,29)(32,35,43,40)>;
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), (2,28,73,47)(3,55,72,20)(4,9,71,66)(5,36,70,39)(6,63,69,12)(7,17,68,58)(8,44,67,31)(10,25,65,50)(11,52,64,23)(13,33,62,42)(14,60,61,15)(16,41,59,34)(18,22,57,53)(19,49,56,26)(21,30,54,45)(24,38,51,37)(27,46,48,29)(32,35,43,40) );
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)], [(2,28,73,47),(3,55,72,20),(4,9,71,66),(5,36,70,39),(6,63,69,12),(7,17,68,58),(8,44,67,31),(10,25,65,50),(11,52,64,23),(13,33,62,42),(14,60,61,15),(16,41,59,34),(18,22,57,53),(19,49,56,26),(21,30,54,45),(24,38,51,37),(27,46,48,29),(32,35,43,40)]])
Matrix representation of C73⋊C4 ►in GL4(𝔽293) generated by
74 | 1 | 0 | 0 |
259 | 0 | 1 | 0 |
120 | 0 | 0 | 1 |
154 | 58 | 196 | 170 |
107 | 32 | 31 | 87 |
55 | 171 | 99 | 43 |
191 | 262 | 101 | 277 |
56 | 82 | 80 | 207 |
G:=sub<GL(4,GF(293))| [74,259,120,154,1,0,0,58,0,1,0,196,0,0,1,170],[107,55,191,56,32,171,262,82,31,99,101,80,87,43,277,207] >;
C73⋊C4 in GAP, Magma, Sage, TeX
C_{73}\rtimes C_4
% in TeX
G:=Group("C73:C4");
// GroupNames label
G:=SmallGroup(292,3);
// by ID
G=gap.SmallGroup(292,3);
# by ID
G:=PCGroup([3,-2,-2,-73,6,974,1301]);
// Polycyclic
G:=Group<a,b|a^73=b^4=1,b*a*b^-1=a^46>;
// generators/relations
Export
Subgroup lattice of C73⋊C4 in TeX
Character table of C73⋊C4 in TeX