metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary
Aliases: C73⋊C3, SmallGroup(219,1)
Series: Derived ►Chief ►Lower central ►Upper central
C73 — C73⋊C3 |
Generators and relations for C73⋊C3
G = < a,b | a73=b3=1, bab-1=a64 >
Character table of C73⋊C3
class | 1 | 3A | 3B | 73A | 73B | 73C | 73D | 73E | 73F | 73G | 73H | 73I | 73J | 73K | 73L | 73M | 73N | 73O | 73P | 73Q | 73R | 73S | 73T | 73U | 73V | 73W | 73X | |
size | 1 | 73 | 73 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
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 | trivial |
ρ2 | 1 | ζ32 | ζ3 | 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 3 |
ρ3 | 1 | ζ3 | ζ32 | 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 3 |
ρ4 | 3 | 0 | 0 | ζ7337+ζ7332+ζ734 | ζ7367+ζ7354+ζ7325 | ζ7331+ζ7329+ζ7313 | ζ7364+ζ738+ζ73 | ζ7362+ζ7358+ζ7326 | ζ7338+ζ7323+ζ7312 | ζ7339+ζ7320+ζ7314 | ζ7355+ζ7316+ζ732 | ζ7366+ζ7363+ζ7317 | ζ7352+ζ7351+ζ7343 | ζ7347+ζ7315+ζ7311 | ζ7346+ζ7324+ζ733 | ζ7340+ζ7328+ζ735 | ζ7372+ζ7365+ζ739 | ζ7359+ζ7353+ζ7334 | ζ7369+ζ7341+ζ7336 | ζ7360+ζ7344+ζ7342 | ζ7330+ζ7322+ζ7321 | ζ7371+ζ7357+ζ7318 | ζ7348+ζ7319+ζ736 | ζ7356+ζ7310+ζ737 | ζ7368+ζ7345+ζ7333 | ζ7361+ζ7350+ζ7335 | ζ7370+ζ7349+ζ7327 | complex faithful |
ρ5 | 3 | 0 | 0 | ζ7338+ζ7323+ζ7312 | ζ7355+ζ7316+ζ732 | ζ7339+ζ7320+ζ7314 | ζ7346+ζ7324+ζ733 | ζ7340+ζ7328+ζ735 | ζ7369+ζ7341+ζ7336 | ζ7360+ζ7344+ζ7342 | ζ7348+ζ7319+ζ736 | ζ7352+ζ7351+ζ7343 | ζ7356+ζ7310+ζ737 | ζ7368+ζ7345+ζ7333 | ζ7372+ζ7365+ζ739 | ζ7347+ζ7315+ζ7311 | ζ7370+ζ7349+ζ7327 | ζ7331+ζ7329+ζ7313 | ζ7361+ζ7350+ζ7335 | ζ7359+ζ7353+ζ7334 | ζ7366+ζ7363+ζ7317 | ζ7367+ζ7354+ζ7325 | ζ7371+ζ7357+ζ7318 | ζ7330+ζ7322+ζ7321 | ζ7362+ζ7358+ζ7326 | ζ7337+ζ7332+ζ734 | ζ7364+ζ738+ζ73 | complex faithful |
ρ6 | 3 | 0 | 0 | ζ7361+ζ7350+ζ7335 | ζ7371+ζ7357+ζ7318 | ζ7359+ζ7353+ζ7334 | ζ7370+ζ7349+ζ7327 | ζ7368+ζ7345+ζ7333 | ζ7337+ζ7332+ζ734 | ζ7331+ζ7329+ζ7313 | ζ7367+ζ7354+ζ7325 | ζ7330+ζ7322+ζ7321 | ζ7366+ζ7363+ζ7317 | ζ7340+ζ7328+ζ735 | ζ7364+ζ738+ζ73 | ζ7362+ζ7358+ζ7326 | ζ7346+ζ7324+ζ733 | ζ7360+ζ7344+ζ7342 | ζ7338+ζ7323+ζ7312 | ζ7339+ζ7320+ζ7314 | ζ7356+ζ7310+ζ737 | ζ7348+ζ7319+ζ736 | ζ7355+ζ7316+ζ732 | ζ7352+ζ7351+ζ7343 | ζ7347+ζ7315+ζ7311 | ζ7369+ζ7341+ζ7336 | ζ7372+ζ7365+ζ739 | complex faithful |
ρ7 | 3 | 0 | 0 | ζ7359+ζ7353+ζ7334 | ζ7330+ζ7322+ζ7321 | ζ7364+ζ738+ζ73 | ζ7368+ζ7345+ζ7333 | ζ7355+ζ7316+ζ732 | ζ7331+ζ7329+ζ7313 | ζ7346+ζ7324+ζ733 | ζ7366+ζ7363+ζ7317 | ζ7361+ζ7350+ζ7335 | ζ7337+ζ7332+ζ734 | ζ7371+ζ7357+ζ7318 | ζ7362+ζ7358+ζ7326 | ζ7348+ζ7319+ζ736 | ζ7340+ζ7328+ζ735 | ζ7370+ζ7349+ζ7327 | ζ7339+ζ7320+ζ7314 | ζ7372+ζ7365+ζ739 | ζ7369+ζ7341+ζ7336 | ζ7356+ζ7310+ζ737 | ζ7352+ζ7351+ζ7343 | ζ7338+ζ7323+ζ7312 | ζ7367+ζ7354+ζ7325 | ζ7360+ζ7344+ζ7342 | ζ7347+ζ7315+ζ7311 | complex faithful |
ρ8 | 3 | 0 | 0 | ζ7347+ζ7315+ζ7311 | ζ7339+ζ7320+ζ7314 | ζ7367+ζ7354+ζ7325 | ζ7330+ζ7322+ζ7321 | ζ7361+ζ7350+ζ7335 | ζ7368+ζ7345+ζ7333 | ζ7355+ζ7316+ζ732 | ζ7360+ζ7344+ζ7342 | ζ7372+ζ7365+ζ739 | ζ7370+ζ7349+ζ7327 | ζ7338+ζ7323+ζ7312 | ζ7366+ζ7363+ζ7317 | ζ7337+ζ7332+ζ734 | ζ7352+ζ7351+ζ7343 | ζ7371+ζ7357+ζ7318 | ζ7362+ζ7358+ζ7326 | ζ7348+ζ7319+ζ736 | ζ7346+ζ7324+ζ733 | ζ7331+ζ7329+ζ7313 | ζ7359+ζ7353+ζ7334 | ζ7364+ζ738+ζ73 | ζ7369+ζ7341+ζ7336 | ζ7340+ζ7328+ζ735 | ζ7356+ζ7310+ζ737 | complex faithful |
ρ9 | 3 | 0 | 0 | ζ7340+ζ7328+ζ735 | ζ7331+ζ7329+ζ7313 | ζ7371+ζ7357+ζ7318 | ζ7356+ζ7310+ζ737 | ζ7369+ζ7341+ζ7336 | ζ7347+ζ7315+ζ7311 | ζ7367+ζ7354+ζ7325 | ζ7339+ζ7320+ζ7314 | ζ7346+ζ7324+ζ733 | ζ7372+ζ7365+ζ739 | ζ7337+ζ7332+ζ734 | ζ7330+ζ7322+ζ7321 | ζ7361+ζ7350+ζ7335 | ζ7366+ζ7363+ζ7317 | ζ7348+ζ7319+ζ736 | ζ7368+ζ7345+ζ7333 | ζ7355+ζ7316+ζ732 | ζ7364+ζ738+ζ73 | ζ7359+ζ7353+ζ7334 | ζ7360+ζ7344+ζ7342 | ζ7370+ζ7349+ζ7327 | ζ7338+ζ7323+ζ7312 | ζ7362+ζ7358+ζ7326 | ζ7352+ζ7351+ζ7343 | complex faithful |
ρ10 | 3 | 0 | 0 | ζ7371+ζ7357+ζ7318 | ζ7346+ζ7324+ζ733 | ζ7330+ζ7322+ζ7321 | ζ7369+ζ7341+ζ7336 | ζ7360+ζ7344+ζ7342 | ζ7367+ζ7354+ζ7325 | ζ7366+ζ7363+ζ7317 | ζ7372+ζ7365+ζ739 | ζ7340+ζ7328+ζ735 | ζ7347+ζ7315+ζ7311 | ζ7331+ζ7329+ζ7313 | ζ7361+ζ7350+ζ7335 | ζ7359+ζ7353+ζ7334 | ζ7337+ζ7332+ζ734 | ζ7356+ζ7310+ζ737 | ζ7355+ζ7316+ζ732 | ζ7352+ζ7351+ζ7343 | ζ7362+ζ7358+ζ7326 | ζ7364+ζ738+ζ73 | ζ7370+ζ7349+ζ7327 | ζ7368+ζ7345+ζ7333 | ζ7339+ζ7320+ζ7314 | ζ7348+ζ7319+ζ736 | ζ7338+ζ7323+ζ7312 | complex faithful |
ρ11 | 3 | 0 | 0 | ζ7367+ζ7354+ζ7325 | ζ7372+ζ7365+ζ739 | ζ7366+ζ7363+ζ7317 | ζ7361+ζ7350+ζ7335 | ζ7359+ζ7353+ζ7334 | ζ7355+ζ7316+ζ732 | ζ7352+ζ7351+ζ7343 | ζ7370+ζ7349+ζ7327 | ζ7347+ζ7315+ζ7311 | ζ7368+ζ7345+ζ7333 | ζ7339+ζ7320+ζ7314 | ζ7337+ζ7332+ζ734 | ζ7331+ζ7329+ζ7313 | ζ7338+ζ7323+ζ7312 | ζ7330+ζ7322+ζ7321 | ζ7348+ζ7319+ζ736 | ζ7356+ζ7310+ζ737 | ζ7340+ζ7328+ζ735 | ζ7346+ζ7324+ζ733 | ζ7364+ζ738+ζ73 | ζ7362+ζ7358+ζ7326 | ζ7360+ζ7344+ζ7342 | ζ7371+ζ7357+ζ7318 | ζ7369+ζ7341+ζ7336 | complex faithful |
ρ12 | 3 | 0 | 0 | ζ7330+ζ7322+ζ7321 | ζ7340+ζ7328+ζ735 | ζ7361+ζ7350+ζ7335 | ζ7360+ζ7344+ζ7342 | ζ7370+ζ7349+ζ7327 | ζ7366+ζ7363+ζ7317 | ζ7337+ζ7332+ζ734 | ζ7347+ζ7315+ζ7311 | ζ7371+ζ7357+ζ7318 | ζ7367+ζ7354+ζ7325 | ζ7346+ζ7324+ζ733 | ζ7359+ζ7353+ζ7334 | ζ7364+ζ738+ζ73 | ζ7331+ζ7329+ζ7313 | ζ7369+ζ7341+ζ7336 | ζ7352+ζ7351+ζ7343 | ζ7338+ζ7323+ζ7312 | ζ7348+ζ7319+ζ736 | ζ7362+ζ7358+ζ7326 | ζ7368+ζ7345+ζ7333 | ζ7355+ζ7316+ζ732 | ζ7372+ζ7365+ζ739 | ζ7356+ζ7310+ζ737 | ζ7339+ζ7320+ζ7314 | complex faithful |
ρ13 | 3 | 0 | 0 | ζ7362+ζ7358+ζ7326 | ζ7359+ζ7353+ζ7334 | ζ7348+ζ7319+ζ736 | ζ7352+ζ7351+ζ7343 | ζ7338+ζ7323+ζ7312 | ζ7340+ζ7328+ζ735 | ζ7371+ζ7357+ζ7318 | ζ7331+ζ7329+ζ7313 | ζ7364+ζ738+ζ73 | ζ7346+ζ7324+ζ733 | ζ7361+ζ7350+ζ7335 | ζ7356+ζ7310+ζ737 | ζ7369+ζ7341+ζ7336 | ζ7330+ζ7322+ζ7321 | ζ7355+ζ7316+ζ732 | ζ7347+ζ7315+ζ7311 | ζ7367+ζ7354+ζ7325 | ζ7370+ζ7349+ζ7327 | ζ7360+ζ7344+ζ7342 | ζ7339+ζ7320+ζ7314 | ζ7372+ζ7365+ζ739 | ζ7337+ζ7332+ζ734 | ζ7368+ζ7345+ζ7333 | ζ7366+ζ7363+ζ7317 | complex faithful |
ρ14 | 3 | 0 | 0 | ζ7368+ζ7345+ζ7333 | ζ7360+ζ7344+ζ7342 | ζ7355+ζ7316+ζ732 | ζ7366+ζ7363+ζ7317 | ζ7337+ζ7332+ζ734 | ζ7362+ζ7358+ζ7326 | ζ7348+ζ7319+ζ736 | ζ7359+ζ7353+ζ7334 | ζ7370+ζ7349+ζ7327 | ζ7364+ζ738+ζ73 | ζ7369+ζ7341+ζ7336 | ζ7352+ζ7351+ζ7343 | ζ7338+ζ7323+ζ7312 | ζ7356+ζ7310+ζ737 | ζ7367+ζ7354+ζ7325 | ζ7340+ζ7328+ζ735 | ζ7371+ζ7357+ζ7318 | ζ7372+ζ7365+ζ739 | ζ7339+ζ7320+ζ7314 | ζ7331+ζ7329+ζ7313 | ζ7346+ζ7324+ζ733 | ζ7361+ζ7350+ζ7335 | ζ7347+ζ7315+ζ7311 | ζ7330+ζ7322+ζ7321 | complex faithful |
ρ15 | 3 | 0 | 0 | ζ7369+ζ7341+ζ7336 | ζ7348+ζ7319+ζ736 | ζ7360+ζ7344+ζ7342 | ζ7372+ζ7365+ζ739 | ζ7347+ζ7315+ζ7311 | ζ7361+ζ7350+ζ7335 | ζ7359+ζ7353+ζ7334 | ζ7371+ζ7357+ζ7318 | ζ7356+ζ7310+ζ737 | ζ7330+ζ7322+ζ7321 | ζ7362+ζ7358+ζ7326 | ζ7370+ζ7349+ζ7327 | ζ7368+ζ7345+ζ7333 | ζ7364+ζ738+ζ73 | ζ7339+ζ7320+ζ7314 | ζ7337+ζ7332+ζ734 | ζ7331+ζ7329+ζ7313 | ζ7352+ζ7351+ζ7343 | ζ7355+ζ7316+ζ732 | ζ7367+ζ7354+ζ7325 | ζ7366+ζ7363+ζ7317 | ζ7340+ζ7328+ζ735 | ζ7338+ζ7323+ζ7312 | ζ7346+ζ7324+ζ733 | complex faithful |
ρ16 | 3 | 0 | 0 | ζ7356+ζ7310+ζ737 | ζ7362+ζ7358+ζ7326 | ζ7369+ζ7341+ζ7336 | ζ7339+ζ7320+ζ7314 | ζ7372+ζ7365+ζ739 | ζ7330+ζ7322+ζ7321 | ζ7361+ζ7350+ζ7335 | ζ7340+ζ7328+ζ735 | ζ7348+ζ7319+ζ736 | ζ7371+ζ7357+ζ7318 | ζ7364+ζ738+ζ73 | ζ7360+ζ7344+ζ7342 | ζ7370+ζ7349+ζ7327 | ζ7359+ζ7353+ζ7334 | ζ7338+ζ7323+ζ7312 | ζ7366+ζ7363+ζ7317 | ζ7337+ζ7332+ζ734 | ζ7355+ζ7316+ζ732 | ζ7368+ζ7345+ζ7333 | ζ7347+ζ7315+ζ7311 | ζ7367+ζ7354+ζ7325 | ζ7346+ζ7324+ζ733 | ζ7352+ζ7351+ζ7343 | ζ7331+ζ7329+ζ7313 | complex faithful |
ρ17 | 3 | 0 | 0 | ζ7346+ζ7324+ζ733 | ζ7337+ζ7332+ζ734 | ζ7340+ζ7328+ζ735 | ζ7348+ζ7319+ζ736 | ζ7356+ζ7310+ζ737 | ζ7372+ζ7365+ζ739 | ζ7347+ζ7315+ζ7311 | ζ7338+ζ7323+ζ7312 | ζ7331+ζ7329+ζ7313 | ζ7339+ζ7320+ζ7314 | ζ7366+ζ7363+ζ7317 | ζ7371+ζ7357+ζ7318 | ζ7330+ζ7322+ζ7321 | ζ7367+ζ7354+ζ7325 | ζ7362+ζ7358+ζ7326 | ζ7370+ζ7349+ζ7327 | ζ7368+ζ7345+ζ7333 | ζ7359+ζ7353+ζ7334 | ζ7361+ζ7350+ζ7335 | ζ7369+ζ7341+ζ7336 | ζ7360+ζ7344+ζ7342 | ζ7352+ζ7351+ζ7343 | ζ7364+ζ738+ζ73 | ζ7355+ζ7316+ζ732 | complex faithful |
ρ18 | 3 | 0 | 0 | ζ7366+ζ7363+ζ7317 | ζ7347+ζ7315+ζ7311 | ζ7337+ζ7332+ζ734 | ζ7359+ζ7353+ζ7334 | ζ7364+ζ738+ζ73 | ζ7352+ζ7351+ζ7343 | ζ7338+ζ7323+ζ7312 | ζ7368+ζ7345+ζ7333 | ζ7367+ζ7354+ζ7325 | ζ7355+ζ7316+ζ732 | ζ7372+ζ7365+ζ739 | ζ7331+ζ7329+ζ7313 | ζ7346+ζ7324+ζ733 | ζ7339+ζ7320+ζ7314 | ζ7361+ζ7350+ζ7335 | ζ7356+ζ7310+ζ737 | ζ7369+ζ7341+ζ7336 | ζ7371+ζ7357+ζ7318 | ζ7340+ζ7328+ζ735 | ζ7362+ζ7358+ζ7326 | ζ7348+ζ7319+ζ736 | ζ7370+ζ7349+ζ7327 | ζ7330+ζ7322+ζ7321 | ζ7360+ζ7344+ζ7342 | complex faithful |
ρ19 | 3 | 0 | 0 | ζ7364+ζ738+ζ73 | ζ7361+ζ7350+ζ7335 | ζ7362+ζ7358+ζ7326 | ζ7355+ζ7316+ζ732 | ζ7352+ζ7351+ζ7343 | ζ7346+ζ7324+ζ733 | ζ7340+ζ7328+ζ735 | ζ7337+ζ7332+ζ734 | ζ7359+ζ7353+ζ7334 | ζ7331+ζ7329+ζ7313 | ζ7330+ζ7322+ζ7321 | ζ7348+ζ7319+ζ736 | ζ7356+ζ7310+ζ737 | ζ7371+ζ7357+ζ7318 | ζ7368+ζ7345+ζ7333 | ζ7372+ζ7365+ζ739 | ζ7347+ζ7315+ζ7311 | ζ7360+ζ7344+ζ7342 | ζ7369+ζ7341+ζ7336 | ζ7338+ζ7323+ζ7312 | ζ7339+ζ7320+ζ7314 | ζ7366+ζ7363+ζ7317 | ζ7370+ζ7349+ζ7327 | ζ7367+ζ7354+ζ7325 | complex faithful |
ρ20 | 3 | 0 | 0 | ζ7352+ζ7351+ζ7343 | ζ7368+ζ7345+ζ7333 | ζ7338+ζ7323+ζ7312 | ζ7331+ζ7329+ζ7313 | ζ7346+ζ7324+ζ733 | ζ7356+ζ7310+ζ737 | ζ7369+ζ7341+ζ7336 | ζ7362+ζ7358+ζ7326 | ζ7355+ζ7316+ζ732 | ζ7348+ζ7319+ζ736 | ζ7370+ζ7349+ζ7327 | ζ7339+ζ7320+ζ7314 | ζ7372+ζ7365+ζ739 | ζ7360+ζ7344+ζ7342 | ζ7337+ζ7332+ζ734 | ζ7330+ζ7322+ζ7321 | ζ7361+ζ7350+ζ7335 | ζ7367+ζ7354+ζ7325 | ζ7347+ζ7315+ζ7311 | ζ7340+ζ7328+ζ735 | ζ7371+ζ7357+ζ7318 | ζ7364+ζ738+ζ73 | ζ7366+ζ7363+ζ7317 | ζ7359+ζ7353+ζ7334 | complex faithful |
ρ21 | 3 | 0 | 0 | ζ7339+ζ7320+ζ7314 | ζ7352+ζ7351+ζ7343 | ζ7372+ζ7365+ζ739 | ζ7340+ζ7328+ζ735 | ζ7371+ζ7357+ζ7318 | ζ7360+ζ7344+ζ7342 | ζ7370+ζ7349+ζ7327 | ζ7356+ζ7310+ζ737 | ζ7338+ζ7323+ζ7312 | ζ7369+ζ7341+ζ7336 | ζ7355+ζ7316+ζ732 | ζ7347+ζ7315+ζ7311 | ζ7367+ζ7354+ζ7325 | ζ7368+ζ7345+ζ7333 | ζ7346+ζ7324+ζ733 | ζ7359+ζ7353+ζ7334 | ζ7364+ζ738+ζ73 | ζ7337+ζ7332+ζ734 | ζ7366+ζ7363+ζ7317 | ζ7330+ζ7322+ζ7321 | ζ7361+ζ7350+ζ7335 | ζ7348+ζ7319+ζ736 | ζ7331+ζ7329+ζ7313 | ζ7362+ζ7358+ζ7326 | complex faithful |
ρ22 | 3 | 0 | 0 | ζ7348+ζ7319+ζ736 | ζ7364+ζ738+ζ73 | ζ7356+ζ7310+ζ737 | ζ7338+ζ7323+ζ7312 | ζ7339+ζ7320+ζ7314 | ζ7371+ζ7357+ζ7318 | ζ7330+ζ7322+ζ7321 | ζ7346+ζ7324+ζ733 | ζ7362+ζ7358+ζ7326 | ζ7340+ζ7328+ζ735 | ζ7359+ζ7353+ζ7334 | ζ7369+ζ7341+ζ7336 | ζ7360+ζ7344+ζ7342 | ζ7361+ζ7350+ζ7335 | ζ7352+ζ7351+ζ7343 | ζ7367+ζ7354+ζ7325 | ζ7366+ζ7363+ζ7317 | ζ7368+ζ7345+ζ7333 | ζ7370+ζ7349+ζ7327 | ζ7372+ζ7365+ζ739 | ζ7347+ζ7315+ζ7311 | ζ7331+ζ7329+ζ7313 | ζ7355+ζ7316+ζ732 | ζ7337+ζ7332+ζ734 | complex faithful |
ρ23 | 3 | 0 | 0 | ζ7355+ζ7316+ζ732 | ζ7370+ζ7349+ζ7327 | ζ7352+ζ7351+ζ7343 | ζ7337+ζ7332+ζ734 | ζ7331+ζ7329+ζ7313 | ζ7348+ζ7319+ζ736 | ζ7356+ζ7310+ζ737 | ζ7364+ζ738+ζ73 | ζ7368+ζ7345+ζ7333 | ζ7362+ζ7358+ζ7326 | ζ7360+ζ7344+ζ7342 | ζ7338+ζ7323+ζ7312 | ζ7339+ζ7320+ζ7314 | ζ7369+ζ7341+ζ7336 | ζ7366+ζ7363+ζ7317 | ζ7371+ζ7357+ζ7318 | ζ7330+ζ7322+ζ7321 | ζ7347+ζ7315+ζ7311 | ζ7372+ζ7365+ζ739 | ζ7346+ζ7324+ζ733 | ζ7340+ζ7328+ζ735 | ζ7359+ζ7353+ζ7334 | ζ7367+ζ7354+ζ7325 | ζ7361+ζ7350+ζ7335 | complex faithful |
ρ24 | 3 | 0 | 0 | ζ7360+ζ7344+ζ7342 | ζ7356+ζ7310+ζ737 | ζ7370+ζ7349+ζ7327 | ζ7347+ζ7315+ζ7311 | ζ7367+ζ7354+ζ7325 | ζ7359+ζ7353+ζ7334 | ζ7364+ζ738+ζ73 | ζ7330+ζ7322+ζ7321 | ζ7369+ζ7341+ζ7336 | ζ7361+ζ7350+ζ7335 | ζ7348+ζ7319+ζ736 | ζ7368+ζ7345+ζ7333 | ζ7355+ζ7316+ζ732 | ζ7362+ζ7358+ζ7326 | ζ7372+ζ7365+ζ739 | ζ7331+ζ7329+ζ7313 | ζ7346+ζ7324+ζ733 | ζ7338+ζ7323+ζ7312 | ζ7352+ζ7351+ζ7343 | ζ7366+ζ7363+ζ7317 | ζ7337+ζ7332+ζ734 | ζ7371+ζ7357+ζ7318 | ζ7339+ζ7320+ζ7314 | ζ7340+ζ7328+ζ735 | complex faithful |
ρ25 | 3 | 0 | 0 | ζ7331+ζ7329+ζ7313 | ζ7366+ζ7363+ζ7317 | ζ7346+ζ7324+ζ733 | ζ7362+ζ7358+ζ7326 | ζ7348+ζ7319+ζ736 | ζ7339+ζ7320+ζ7314 | ζ7372+ζ7365+ζ739 | ζ7352+ζ7351+ζ7343 | ζ7337+ζ7332+ζ734 | ζ7338+ζ7323+ζ7312 | ζ7367+ζ7354+ζ7325 | ζ7340+ζ7328+ζ735 | ζ7371+ζ7357+ζ7318 | ζ7347+ζ7315+ζ7311 | ζ7364+ζ738+ζ73 | ζ7360+ζ7344+ζ7342 | ζ7370+ζ7349+ζ7327 | ζ7361+ζ7350+ζ7335 | ζ7330+ζ7322+ζ7321 | ζ7356+ζ7310+ζ737 | ζ7369+ζ7341+ζ7336 | ζ7355+ζ7316+ζ732 | ζ7359+ζ7353+ζ7334 | ζ7368+ζ7345+ζ7333 | complex faithful |
ρ26 | 3 | 0 | 0 | ζ7372+ζ7365+ζ739 | ζ7338+ζ7323+ζ7312 | ζ7347+ζ7315+ζ7311 | ζ7371+ζ7357+ζ7318 | ζ7330+ζ7322+ζ7321 | ζ7370+ζ7349+ζ7327 | ζ7368+ζ7345+ζ7333 | ζ7369+ζ7341+ζ7336 | ζ7339+ζ7320+ζ7314 | ζ7360+ζ7344+ζ7342 | ζ7352+ζ7351+ζ7343 | ζ7367+ζ7354+ζ7325 | ζ7366+ζ7363+ζ7317 | ζ7355+ζ7316+ζ732 | ζ7340+ζ7328+ζ735 | ζ7364+ζ738+ζ73 | ζ7362+ζ7358+ζ7326 | ζ7331+ζ7329+ζ7313 | ζ7337+ζ7332+ζ734 | ζ7361+ζ7350+ζ7335 | ζ7359+ζ7353+ζ7334 | ζ7356+ζ7310+ζ737 | ζ7346+ζ7324+ζ733 | ζ7348+ζ7319+ζ736 | complex faithful |
ρ27 | 3 | 0 | 0 | ζ7370+ζ7349+ζ7327 | ζ7369+ζ7341+ζ7336 | ζ7368+ζ7345+ζ7333 | ζ7367+ζ7354+ζ7325 | ζ7366+ζ7363+ζ7317 | ζ7364+ζ738+ζ73 | ζ7362+ζ7358+ζ7326 | ζ7361+ζ7350+ζ7335 | ζ7360+ζ7344+ζ7342 | ζ7359+ζ7353+ζ7334 | ζ7356+ζ7310+ζ737 | ζ7355+ζ7316+ζ732 | ζ7352+ζ7351+ζ7343 | ζ7348+ζ7319+ζ736 | ζ7347+ζ7315+ζ7311 | ζ7346+ζ7324+ζ733 | ζ7340+ζ7328+ζ735 | ζ7339+ζ7320+ζ7314 | ζ7338+ζ7323+ζ7312 | ζ7337+ζ7332+ζ734 | ζ7331+ζ7329+ζ7313 | ζ7330+ζ7322+ζ7321 | ζ7372+ζ7365+ζ739 | ζ7371+ζ7357+ζ7318 | complex 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 9 65)(3 17 56)(4 25 47)(5 33 38)(6 41 29)(7 49 20)(8 57 11)(10 73 66)(12 16 48)(13 24 39)(14 32 30)(15 40 21)(18 64 67)(19 72 58)(22 23 31)(26 55 68)(27 63 59)(28 71 50)(34 46 69)(35 54 60)(36 62 51)(37 70 42)(43 45 61)(44 53 52)
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), (2,9,65)(3,17,56)(4,25,47)(5,33,38)(6,41,29)(7,49,20)(8,57,11)(10,73,66)(12,16,48)(13,24,39)(14,32,30)(15,40,21)(18,64,67)(19,72,58)(22,23,31)(26,55,68)(27,63,59)(28,71,50)(34,46,69)(35,54,60)(36,62,51)(37,70,42)(43,45,61)(44,53,52)>;
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), (2,9,65)(3,17,56)(4,25,47)(5,33,38)(6,41,29)(7,49,20)(8,57,11)(10,73,66)(12,16,48)(13,24,39)(14,32,30)(15,40,21)(18,64,67)(19,72,58)(22,23,31)(26,55,68)(27,63,59)(28,71,50)(34,46,69)(35,54,60)(36,62,51)(37,70,42)(43,45,61)(44,53,52) );
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)], [(2,9,65),(3,17,56),(4,25,47),(5,33,38),(6,41,29),(7,49,20),(8,57,11),(10,73,66),(12,16,48),(13,24,39),(14,32,30),(15,40,21),(18,64,67),(19,72,58),(22,23,31),(26,55,68),(27,63,59),(28,71,50),(34,46,69),(35,54,60),(36,62,51),(37,70,42),(43,45,61),(44,53,52)]])
C73⋊C3 is a maximal subgroup of
C73⋊C6
Matrix representation of C73⋊C3 ►in GL3(𝔽439) generated by
130 | 1 | 0 |
433 | 0 | 1 |
212 | 220 | 122 |
27 | 104 | 113 |
386 | 303 | 118 |
416 | 242 | 109 |
G:=sub<GL(3,GF(439))| [130,433,212,1,0,220,0,1,122],[27,386,416,104,303,242,113,118,109] >;
C73⋊C3 in GAP, Magma, Sage, TeX
C_{73}\rtimes C_3
% in TeX
G:=Group("C73:C3");
// GroupNames label
G:=SmallGroup(219,1);
// by ID
G=gap.SmallGroup(219,1);
# by ID
G:=PCGroup([2,-3,-73,97]);
// Polycyclic
G:=Group<a,b|a^73=b^3=1,b*a*b^-1=a^64>;
// generators/relations
Export
Subgroup lattice of C73⋊C3 in TeX
Character table of C73⋊C3 in TeX