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G = C73⋊C3  order 219 = 3·73

The semidirect product of C73 and C3 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C73⋊C3, SmallGroup(219,1)

Series: Derived ►Chief ►Lower central ►Upper central

C1 — C73 — C73⋊C3
C1 — C73 — C73⋊C3
C73 — C73⋊C3
C1

Generators and relations for C73⋊C3
 G = < a,b | a73=b3=1, bab-1=a64 >

73C3

Character table of C73⋊C3

 class 13A3B73A73B73C73D73E73F73G73H73I73J73K73L73M73N73O73P73Q73R73S73T73U73V73W73X
 size 17373333333333333333333333333
ρ1111111111111111111111111111    trivial
ρ21ζ32ζ3111111111111111111111111    linear of order 3
ρ31ζ3ζ32111111111111111111111111    linear of order 3
ρ4300ζ7337+ζ7332+ζ734ζ7367+ζ7354+ζ7325ζ7331+ζ7329+ζ7313ζ7364+ζ738+ζ73ζ7362+ζ7358+ζ7326ζ7338+ζ7323+ζ7312ζ7339+ζ7320+ζ7314ζ7355+ζ7316+ζ732ζ7366+ζ7363+ζ7317ζ7352+ζ7351+ζ7343ζ7347+ζ7315+ζ7311ζ7346+ζ7324+ζ733ζ7340+ζ7328+ζ735ζ7372+ζ7365+ζ739ζ7359+ζ7353+ζ7334ζ7369+ζ7341+ζ7336ζ7360+ζ7344+ζ7342ζ7330+ζ7322+ζ7321ζ7371+ζ7357+ζ7318ζ7348+ζ7319+ζ736ζ7356+ζ7310+ζ737ζ7368+ζ7345+ζ7333ζ7361+ζ7350+ζ7335ζ7370+ζ7349+ζ7327    complex faithful
ρ5300ζ7338+ζ7323+ζ7312ζ7355+ζ7316+ζ732ζ7339+ζ7320+ζ7314ζ7346+ζ7324+ζ733ζ7340+ζ7328+ζ735ζ7369+ζ7341+ζ7336ζ7360+ζ7344+ζ7342ζ7348+ζ7319+ζ736ζ7352+ζ7351+ζ7343ζ7356+ζ7310+ζ737ζ7368+ζ7345+ζ7333ζ7372+ζ7365+ζ739ζ7347+ζ7315+ζ7311ζ7370+ζ7349+ζ7327ζ7331+ζ7329+ζ7313ζ7361+ζ7350+ζ7335ζ7359+ζ7353+ζ7334ζ7366+ζ7363+ζ7317ζ7367+ζ7354+ζ7325ζ7371+ζ7357+ζ7318ζ7330+ζ7322+ζ7321ζ7362+ζ7358+ζ7326ζ7337+ζ7332+ζ734ζ7364+ζ738+ζ73    complex faithful
ρ6300ζ7361+ζ7350+ζ7335ζ7371+ζ7357+ζ7318ζ7359+ζ7353+ζ7334ζ7370+ζ7349+ζ7327ζ7368+ζ7345+ζ7333ζ7337+ζ7332+ζ734ζ7331+ζ7329+ζ7313ζ7367+ζ7354+ζ7325ζ7330+ζ7322+ζ7321ζ7366+ζ7363+ζ7317ζ7340+ζ7328+ζ735ζ7364+ζ738+ζ73ζ7362+ζ7358+ζ7326ζ7346+ζ7324+ζ733ζ7360+ζ7344+ζ7342ζ7338+ζ7323+ζ7312ζ7339+ζ7320+ζ7314ζ7356+ζ7310+ζ737ζ7348+ζ7319+ζ736ζ7355+ζ7316+ζ732ζ7352+ζ7351+ζ7343ζ7347+ζ7315+ζ7311ζ7369+ζ7341+ζ7336ζ7372+ζ7365+ζ739    complex faithful
ρ7300ζ7359+ζ7353+ζ7334ζ7330+ζ7322+ζ7321ζ7364+ζ738+ζ73ζ7368+ζ7345+ζ7333ζ7355+ζ7316+ζ732ζ7331+ζ7329+ζ7313ζ7346+ζ7324+ζ733ζ7366+ζ7363+ζ7317ζ7361+ζ7350+ζ7335ζ7337+ζ7332+ζ734ζ7371+ζ7357+ζ7318ζ7362+ζ7358+ζ7326ζ7348+ζ7319+ζ736ζ7340+ζ7328+ζ735ζ7370+ζ7349+ζ7327ζ7339+ζ7320+ζ7314ζ7372+ζ7365+ζ739ζ7369+ζ7341+ζ7336ζ7356+ζ7310+ζ737ζ7352+ζ7351+ζ7343ζ7338+ζ7323+ζ7312ζ7367+ζ7354+ζ7325ζ7360+ζ7344+ζ7342ζ7347+ζ7315+ζ7311    complex faithful
ρ8300ζ7347+ζ7315+ζ7311ζ7339+ζ7320+ζ7314ζ7367+ζ7354+ζ7325ζ7330+ζ7322+ζ7321ζ7361+ζ7350+ζ7335ζ7368+ζ7345+ζ7333ζ7355+ζ7316+ζ732ζ7360+ζ7344+ζ7342ζ7372+ζ7365+ζ739ζ7370+ζ7349+ζ7327ζ7338+ζ7323+ζ7312ζ7366+ζ7363+ζ7317ζ7337+ζ7332+ζ734ζ7352+ζ7351+ζ7343ζ7371+ζ7357+ζ7318ζ7362+ζ7358+ζ7326ζ7348+ζ7319+ζ736ζ7346+ζ7324+ζ733ζ7331+ζ7329+ζ7313ζ7359+ζ7353+ζ7334ζ7364+ζ738+ζ73ζ7369+ζ7341+ζ7336ζ7340+ζ7328+ζ735ζ7356+ζ7310+ζ737    complex faithful
ρ9300ζ7340+ζ7328+ζ735ζ7331+ζ7329+ζ7313ζ7371+ζ7357+ζ7318ζ7356+ζ7310+ζ737ζ7369+ζ7341+ζ7336ζ7347+ζ7315+ζ7311ζ7367+ζ7354+ζ7325ζ7339+ζ7320+ζ7314ζ7346+ζ7324+ζ733ζ7372+ζ7365+ζ739ζ7337+ζ7332+ζ734ζ7330+ζ7322+ζ7321ζ7361+ζ7350+ζ7335ζ7366+ζ7363+ζ7317ζ7348+ζ7319+ζ736ζ7368+ζ7345+ζ7333ζ7355+ζ7316+ζ732ζ7364+ζ738+ζ73ζ7359+ζ7353+ζ7334ζ7360+ζ7344+ζ7342ζ7370+ζ7349+ζ7327ζ7338+ζ7323+ζ7312ζ7362+ζ7358+ζ7326ζ7352+ζ7351+ζ7343    complex faithful
ρ10300ζ7371+ζ7357+ζ7318ζ7346+ζ7324+ζ733ζ7330+ζ7322+ζ7321ζ7369+ζ7341+ζ7336ζ7360+ζ7344+ζ7342ζ7367+ζ7354+ζ7325ζ7366+ζ7363+ζ7317ζ7372+ζ7365+ζ739ζ7340+ζ7328+ζ735ζ7347+ζ7315+ζ7311ζ7331+ζ7329+ζ7313ζ7361+ζ7350+ζ7335ζ7359+ζ7353+ζ7334ζ7337+ζ7332+ζ734ζ7356+ζ7310+ζ737ζ7355+ζ7316+ζ732ζ7352+ζ7351+ζ7343ζ7362+ζ7358+ζ7326ζ7364+ζ738+ζ73ζ7370+ζ7349+ζ7327ζ7368+ζ7345+ζ7333ζ7339+ζ7320+ζ7314ζ7348+ζ7319+ζ736ζ7338+ζ7323+ζ7312    complex faithful
ρ11300ζ7367+ζ7354+ζ7325ζ7372+ζ7365+ζ739ζ7366+ζ7363+ζ7317ζ7361+ζ7350+ζ7335ζ7359+ζ7353+ζ7334ζ7355+ζ7316+ζ732ζ7352+ζ7351+ζ7343ζ7370+ζ7349+ζ7327ζ7347+ζ7315+ζ7311ζ7368+ζ7345+ζ7333ζ7339+ζ7320+ζ7314ζ7337+ζ7332+ζ734ζ7331+ζ7329+ζ7313ζ7338+ζ7323+ζ7312ζ7330+ζ7322+ζ7321ζ7348+ζ7319+ζ736ζ7356+ζ7310+ζ737ζ7340+ζ7328+ζ735ζ7346+ζ7324+ζ733ζ7364+ζ738+ζ73ζ7362+ζ7358+ζ7326ζ7360+ζ7344+ζ7342ζ7371+ζ7357+ζ7318ζ7369+ζ7341+ζ7336    complex faithful
ρ12300ζ7330+ζ7322+ζ7321ζ7340+ζ7328+ζ735ζ7361+ζ7350+ζ7335ζ7360+ζ7344+ζ7342ζ7370+ζ7349+ζ7327ζ7366+ζ7363+ζ7317ζ7337+ζ7332+ζ734ζ7347+ζ7315+ζ7311ζ7371+ζ7357+ζ7318ζ7367+ζ7354+ζ7325ζ7346+ζ7324+ζ733ζ7359+ζ7353+ζ7334ζ7364+ζ738+ζ73ζ7331+ζ7329+ζ7313ζ7369+ζ7341+ζ7336ζ7352+ζ7351+ζ7343ζ7338+ζ7323+ζ7312ζ7348+ζ7319+ζ736ζ7362+ζ7358+ζ7326ζ7368+ζ7345+ζ7333ζ7355+ζ7316+ζ732ζ7372+ζ7365+ζ739ζ7356+ζ7310+ζ737ζ7339+ζ7320+ζ7314    complex faithful
ρ13300ζ7362+ζ7358+ζ7326ζ7359+ζ7353+ζ7334ζ7348+ζ7319+ζ736ζ7352+ζ7351+ζ7343ζ7338+ζ7323+ζ7312ζ7340+ζ7328+ζ735ζ7371+ζ7357+ζ7318ζ7331+ζ7329+ζ7313ζ7364+ζ738+ζ73ζ7346+ζ7324+ζ733ζ7361+ζ7350+ζ7335ζ7356+ζ7310+ζ737ζ7369+ζ7341+ζ7336ζ7330+ζ7322+ζ7321ζ7355+ζ7316+ζ732ζ7347+ζ7315+ζ7311ζ7367+ζ7354+ζ7325ζ7370+ζ7349+ζ7327ζ7360+ζ7344+ζ7342ζ7339+ζ7320+ζ7314ζ7372+ζ7365+ζ739ζ7337+ζ7332+ζ734ζ7368+ζ7345+ζ7333ζ7366+ζ7363+ζ7317    complex faithful
ρ14300ζ7368+ζ7345+ζ7333ζ7360+ζ7344+ζ7342ζ7355+ζ7316+ζ732ζ7366+ζ7363+ζ7317ζ7337+ζ7332+ζ734ζ7362+ζ7358+ζ7326ζ7348+ζ7319+ζ736ζ7359+ζ7353+ζ7334ζ7370+ζ7349+ζ7327ζ7364+ζ738+ζ73ζ7369+ζ7341+ζ7336ζ7352+ζ7351+ζ7343ζ7338+ζ7323+ζ7312ζ7356+ζ7310+ζ737ζ7367+ζ7354+ζ7325ζ7340+ζ7328+ζ735ζ7371+ζ7357+ζ7318ζ7372+ζ7365+ζ739ζ7339+ζ7320+ζ7314ζ7331+ζ7329+ζ7313ζ7346+ζ7324+ζ733ζ7361+ζ7350+ζ7335ζ7347+ζ7315+ζ7311ζ7330+ζ7322+ζ7321    complex faithful
ρ15300ζ7369+ζ7341+ζ7336ζ7348+ζ7319+ζ736ζ7360+ζ7344+ζ7342ζ7372+ζ7365+ζ739ζ7347+ζ7315+ζ7311ζ7361+ζ7350+ζ7335ζ7359+ζ7353+ζ7334ζ7371+ζ7357+ζ7318ζ7356+ζ7310+ζ737ζ7330+ζ7322+ζ7321ζ7362+ζ7358+ζ7326ζ7370+ζ7349+ζ7327ζ7368+ζ7345+ζ7333ζ7364+ζ738+ζ73ζ7339+ζ7320+ζ7314ζ7337+ζ7332+ζ734ζ7331+ζ7329+ζ7313ζ7352+ζ7351+ζ7343ζ7355+ζ7316+ζ732ζ7367+ζ7354+ζ7325ζ7366+ζ7363+ζ7317ζ7340+ζ7328+ζ735ζ7338+ζ7323+ζ7312ζ7346+ζ7324+ζ733    complex faithful
ρ16300ζ7356+ζ7310+ζ737ζ7362+ζ7358+ζ7326ζ7369+ζ7341+ζ7336ζ7339+ζ7320+ζ7314ζ7372+ζ7365+ζ739ζ7330+ζ7322+ζ7321ζ7361+ζ7350+ζ7335ζ7340+ζ7328+ζ735ζ7348+ζ7319+ζ736ζ7371+ζ7357+ζ7318ζ7364+ζ738+ζ73ζ7360+ζ7344+ζ7342ζ7370+ζ7349+ζ7327ζ7359+ζ7353+ζ7334ζ7338+ζ7323+ζ7312ζ7366+ζ7363+ζ7317ζ7337+ζ7332+ζ734ζ7355+ζ7316+ζ732ζ7368+ζ7345+ζ7333ζ7347+ζ7315+ζ7311ζ7367+ζ7354+ζ7325ζ7346+ζ7324+ζ733ζ7352+ζ7351+ζ7343ζ7331+ζ7329+ζ7313    complex faithful
ρ17300ζ7346+ζ7324+ζ733ζ7337+ζ7332+ζ734ζ7340+ζ7328+ζ735ζ7348+ζ7319+ζ736ζ7356+ζ7310+ζ737ζ7372+ζ7365+ζ739ζ7347+ζ7315+ζ7311ζ7338+ζ7323+ζ7312ζ7331+ζ7329+ζ7313ζ7339+ζ7320+ζ7314ζ7366+ζ7363+ζ7317ζ7371+ζ7357+ζ7318ζ7330+ζ7322+ζ7321ζ7367+ζ7354+ζ7325ζ7362+ζ7358+ζ7326ζ7370+ζ7349+ζ7327ζ7368+ζ7345+ζ7333ζ7359+ζ7353+ζ7334ζ7361+ζ7350+ζ7335ζ7369+ζ7341+ζ7336ζ7360+ζ7344+ζ7342ζ7352+ζ7351+ζ7343ζ7364+ζ738+ζ73ζ7355+ζ7316+ζ732    complex faithful
ρ18300ζ7366+ζ7363+ζ7317ζ7347+ζ7315+ζ7311ζ7337+ζ7332+ζ734ζ7359+ζ7353+ζ7334ζ7364+ζ738+ζ73ζ7352+ζ7351+ζ7343ζ7338+ζ7323+ζ7312ζ7368+ζ7345+ζ7333ζ7367+ζ7354+ζ7325ζ7355+ζ7316+ζ732ζ7372+ζ7365+ζ739ζ7331+ζ7329+ζ7313ζ7346+ζ7324+ζ733ζ7339+ζ7320+ζ7314ζ7361+ζ7350+ζ7335ζ7356+ζ7310+ζ737ζ7369+ζ7341+ζ7336ζ7371+ζ7357+ζ7318ζ7340+ζ7328+ζ735ζ7362+ζ7358+ζ7326ζ7348+ζ7319+ζ736ζ7370+ζ7349+ζ7327ζ7330+ζ7322+ζ7321ζ7360+ζ7344+ζ7342    complex faithful
ρ19300ζ7364+ζ738+ζ73ζ7361+ζ7350+ζ7335ζ7362+ζ7358+ζ7326ζ7355+ζ7316+ζ732ζ7352+ζ7351+ζ7343ζ7346+ζ7324+ζ733ζ7340+ζ7328+ζ735ζ7337+ζ7332+ζ734ζ7359+ζ7353+ζ7334ζ7331+ζ7329+ζ7313ζ7330+ζ7322+ζ7321ζ7348+ζ7319+ζ736ζ7356+ζ7310+ζ737ζ7371+ζ7357+ζ7318ζ7368+ζ7345+ζ7333ζ7372+ζ7365+ζ739ζ7347+ζ7315+ζ7311ζ7360+ζ7344+ζ7342ζ7369+ζ7341+ζ7336ζ7338+ζ7323+ζ7312ζ7339+ζ7320+ζ7314ζ7366+ζ7363+ζ7317ζ7370+ζ7349+ζ7327ζ7367+ζ7354+ζ7325    complex faithful
ρ20300ζ7352+ζ7351+ζ7343ζ7368+ζ7345+ζ7333ζ7338+ζ7323+ζ7312ζ7331+ζ7329+ζ7313ζ7346+ζ7324+ζ733ζ7356+ζ7310+ζ737ζ7369+ζ7341+ζ7336ζ7362+ζ7358+ζ7326ζ7355+ζ7316+ζ732ζ7348+ζ7319+ζ736ζ7370+ζ7349+ζ7327ζ7339+ζ7320+ζ7314ζ7372+ζ7365+ζ739ζ7360+ζ7344+ζ7342ζ7337+ζ7332+ζ734ζ7330+ζ7322+ζ7321ζ7361+ζ7350+ζ7335ζ7367+ζ7354+ζ7325ζ7347+ζ7315+ζ7311ζ7340+ζ7328+ζ735ζ7371+ζ7357+ζ7318ζ7364+ζ738+ζ73ζ7366+ζ7363+ζ7317ζ7359+ζ7353+ζ7334    complex faithful
ρ21300ζ7339+ζ7320+ζ7314ζ7352+ζ7351+ζ7343ζ7372+ζ7365+ζ739ζ7340+ζ7328+ζ735ζ7371+ζ7357+ζ7318ζ7360+ζ7344+ζ7342ζ7370+ζ7349+ζ7327ζ7356+ζ7310+ζ737ζ7338+ζ7323+ζ7312ζ7369+ζ7341+ζ7336ζ7355+ζ7316+ζ732ζ7347+ζ7315+ζ7311ζ7367+ζ7354+ζ7325ζ7368+ζ7345+ζ7333ζ7346+ζ7324+ζ733ζ7359+ζ7353+ζ7334ζ7364+ζ738+ζ73ζ7337+ζ7332+ζ734ζ7366+ζ7363+ζ7317ζ7330+ζ7322+ζ7321ζ7361+ζ7350+ζ7335ζ7348+ζ7319+ζ736ζ7331+ζ7329+ζ7313ζ7362+ζ7358+ζ7326    complex faithful
ρ22300ζ7348+ζ7319+ζ736ζ7364+ζ738+ζ73ζ7356+ζ7310+ζ737ζ7338+ζ7323+ζ7312ζ7339+ζ7320+ζ7314ζ7371+ζ7357+ζ7318ζ7330+ζ7322+ζ7321ζ7346+ζ7324+ζ733ζ7362+ζ7358+ζ7326ζ7340+ζ7328+ζ735ζ7359+ζ7353+ζ7334ζ7369+ζ7341+ζ7336ζ7360+ζ7344+ζ7342ζ7361+ζ7350+ζ7335ζ7352+ζ7351+ζ7343ζ7367+ζ7354+ζ7325ζ7366+ζ7363+ζ7317ζ7368+ζ7345+ζ7333ζ7370+ζ7349+ζ7327ζ7372+ζ7365+ζ739ζ7347+ζ7315+ζ7311ζ7331+ζ7329+ζ7313ζ7355+ζ7316+ζ732ζ7337+ζ7332+ζ734    complex faithful
ρ23300ζ7355+ζ7316+ζ732ζ7370+ζ7349+ζ7327ζ7352+ζ7351+ζ7343ζ7337+ζ7332+ζ734ζ7331+ζ7329+ζ7313ζ7348+ζ7319+ζ736ζ7356+ζ7310+ζ737ζ7364+ζ738+ζ73ζ7368+ζ7345+ζ7333ζ7362+ζ7358+ζ7326ζ7360+ζ7344+ζ7342ζ7338+ζ7323+ζ7312ζ7339+ζ7320+ζ7314ζ7369+ζ7341+ζ7336ζ7366+ζ7363+ζ7317ζ7371+ζ7357+ζ7318ζ7330+ζ7322+ζ7321ζ7347+ζ7315+ζ7311ζ7372+ζ7365+ζ739ζ7346+ζ7324+ζ733ζ7340+ζ7328+ζ735ζ7359+ζ7353+ζ7334ζ7367+ζ7354+ζ7325ζ7361+ζ7350+ζ7335    complex faithful
ρ24300ζ7360+ζ7344+ζ7342ζ7356+ζ7310+ζ737ζ7370+ζ7349+ζ7327ζ7347+ζ7315+ζ7311ζ7367+ζ7354+ζ7325ζ7359+ζ7353+ζ7334ζ7364+ζ738+ζ73ζ7330+ζ7322+ζ7321ζ7369+ζ7341+ζ7336ζ7361+ζ7350+ζ7335ζ7348+ζ7319+ζ736ζ7368+ζ7345+ζ7333ζ7355+ζ7316+ζ732ζ7362+ζ7358+ζ7326ζ7372+ζ7365+ζ739ζ7331+ζ7329+ζ7313ζ7346+ζ7324+ζ733ζ7338+ζ7323+ζ7312ζ7352+ζ7351+ζ7343ζ7366+ζ7363+ζ7317ζ7337+ζ7332+ζ734ζ7371+ζ7357+ζ7318ζ7339+ζ7320+ζ7314ζ7340+ζ7328+ζ735    complex faithful
ρ25300ζ7331+ζ7329+ζ7313ζ7366+ζ7363+ζ7317ζ7346+ζ7324+ζ733ζ7362+ζ7358+ζ7326ζ7348+ζ7319+ζ736ζ7339+ζ7320+ζ7314ζ7372+ζ7365+ζ739ζ7352+ζ7351+ζ7343ζ7337+ζ7332+ζ734ζ7338+ζ7323+ζ7312ζ7367+ζ7354+ζ7325ζ7340+ζ7328+ζ735ζ7371+ζ7357+ζ7318ζ7347+ζ7315+ζ7311ζ7364+ζ738+ζ73ζ7360+ζ7344+ζ7342ζ7370+ζ7349+ζ7327ζ7361+ζ7350+ζ7335ζ7330+ζ7322+ζ7321ζ7356+ζ7310+ζ737ζ7369+ζ7341+ζ7336ζ7355+ζ7316+ζ732ζ7359+ζ7353+ζ7334ζ7368+ζ7345+ζ7333    complex faithful
ρ26300ζ7372+ζ7365+ζ739ζ7338+ζ7323+ζ7312ζ7347+ζ7315+ζ7311ζ7371+ζ7357+ζ7318ζ7330+ζ7322+ζ7321ζ7370+ζ7349+ζ7327ζ7368+ζ7345+ζ7333ζ7369+ζ7341+ζ7336ζ7339+ζ7320+ζ7314ζ7360+ζ7344+ζ7342ζ7352+ζ7351+ζ7343ζ7367+ζ7354+ζ7325ζ7366+ζ7363+ζ7317ζ7355+ζ7316+ζ732ζ7340+ζ7328+ζ735ζ7364+ζ738+ζ73ζ7362+ζ7358+ζ7326ζ7331+ζ7329+ζ7313ζ7337+ζ7332+ζ734ζ7361+ζ7350+ζ7335ζ7359+ζ7353+ζ7334ζ7356+ζ7310+ζ737ζ7346+ζ7324+ζ733ζ7348+ζ7319+ζ736    complex faithful
ρ27300ζ7370+ζ7349+ζ7327ζ7369+ζ7341+ζ7336ζ7368+ζ7345+ζ7333ζ7367+ζ7354+ζ7325ζ7366+ζ7363+ζ7317ζ7364+ζ738+ζ73ζ7362+ζ7358+ζ7326ζ7361+ζ7350+ζ7335ζ7360+ζ7344+ζ7342ζ7359+ζ7353+ζ7334ζ7356+ζ7310+ζ737ζ7355+ζ7316+ζ732ζ7352+ζ7351+ζ7343ζ7348+ζ7319+ζ736ζ7347+ζ7315+ζ7311ζ7346+ζ7324+ζ733ζ7340+ζ7328+ζ735ζ7339+ζ7320+ζ7314ζ7338+ζ7323+ζ7312ζ7337+ζ7332+ζ734ζ7331+ζ7329+ζ7313ζ7330+ζ7322+ζ7321ζ7372+ζ7365+ζ739ζ7371+ζ7357+ζ7318    complex faithful

Smallest permutation representation of C73⋊C3
►On 73 points: primitive
Generators in S73
(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

13010
43301
212220122
,
27104113
386303118
416242109
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
 

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Subgroup lattice of C73⋊C3 in TeX
Character table of C73⋊C3 in TeX

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