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## G = C73⋊C4order 292 = 22·73

### The semidirect product of C73 and C4 acting faithfully

Aliases: C73⋊C4, D73.C2, SmallGroup(292,3)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C73 — C73⋊C4
 Chief series C1 — C73 — D73 — C73⋊C4
 Lower central C73 — C73⋊C4
 Upper central C1

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

Smallest permutation representation of C73⋊C4
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 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`

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