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## G = C79⋊C3order 237 = 3·79

### The semidirect product of C79 and C3 acting faithfully

Aliases: C79⋊C3, SmallGroup(237,1)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C79 — C79⋊C3
 Chief series C1 — C79 — C79⋊C3
 Lower central C79 — C79⋊C3
 Upper central C1

Generators and relations for C79⋊C3
G = < a,b | a79=b3=1, bab-1=a55 >

Character table of C79⋊C3

 class 1 3A 3B 79A 79B 79C 79D 79E 79F 79G 79H 79I 79J 79K 79L 79M 79N 79O 79P 79Q 79R 79S 79T 79U 79V 79W 79X 79Y 79Z size 1 79 79 3 3 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 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 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 1 1 linear of order 3 ρ4 3 0 0 ζ7974+ζ7943+ζ7941 ζ7946+ζ7931+ζ792 ζ7942+ζ7919+ζ7918 ζ7969+ζ797+ζ793 ζ7962+ζ7913+ζ794 ζ7964+ζ7950+ζ7944 ζ7938+ζ7936+ζ795 ζ7945+ζ7926+ζ798 ζ7959+ζ7914+ζ796 ζ7957+ζ7954+ζ7947 ζ7977+ζ7948+ζ7933 ζ7949+ζ7921+ζ799 ζ7976+ζ7972+ζ7910 ζ7952+ζ7916+ζ7911 ζ7939+ζ7928+ζ7912 ζ7971+ζ7953+ζ7934 ζ7935+ζ7929+ζ7915 ζ7978+ζ7956+ζ7924 ζ7975+ζ7966+ζ7917 ζ7970+ζ7958+ζ7930 ζ7973+ζ7965+ζ7920 ζ7961+ζ7960+ζ7937 ζ7932+ζ7925+ζ7922 ζ7968+ζ7963+ζ7927 ζ7967+ζ7951+ζ7940 ζ7955+ζ7923+ζ79 complex faithful ρ5 3 0 0 ζ7964+ζ7950+ζ7944 ζ7959+ζ7914+ζ796 ζ7957+ζ7954+ζ7947 ζ7949+ζ7921+ζ799 ζ7939+ζ7928+ζ7912 ζ7971+ζ7953+ζ7934 ζ7935+ζ7929+ζ7915 ζ7978+ζ7956+ζ7924 ζ7942+ζ7919+ζ7918 ζ7962+ζ7913+ζ794 ζ7973+ζ7965+ζ7920 ζ7968+ζ7963+ζ7927 ζ7970+ζ7958+ζ7930 ζ7977+ζ7948+ζ7933 ζ7938+ζ7936+ζ795 ζ7955+ζ7923+ζ79 ζ7945+ζ7926+ζ798 ζ7976+ζ7972+ζ7910 ζ7967+ζ7951+ζ7940 ζ7952+ζ7916+ζ7911 ζ7961+ζ7960+ζ7937 ζ7932+ζ7925+ζ7922 ζ7975+ζ7966+ζ7917 ζ7946+ζ7931+ζ792 ζ7974+ζ7943+ζ7941 ζ7969+ζ797+ζ793 complex faithful ρ6 3 0 0 ζ7977+ζ7948+ζ7933 ζ7964+ζ7950+ζ7944 ζ7955+ζ7923+ζ79 ζ7975+ζ7966+ζ7917 ζ7949+ζ7921+ζ799 ζ7973+ζ7965+ζ7920 ζ7946+ζ7931+ζ792 ζ7942+ζ7919+ζ7918 ζ7971+ζ7953+ζ7934 ζ7969+ζ797+ζ793 ζ7935+ζ7929+ζ7915 ζ7967+ζ7951+ζ7940 ζ7962+ζ7913+ζ794 ζ7938+ζ7936+ζ795 ζ7968+ζ7963+ζ7927 ζ7961+ζ7960+ζ7937 ζ7959+ζ7914+ζ796 ζ7957+ζ7954+ζ7947 ζ7970+ζ7958+ζ7930 ζ7939+ζ7928+ζ7912 ζ7945+ζ7926+ζ798 ζ7978+ζ7956+ζ7924 ζ7976+ζ7972+ζ7910 ζ7974+ζ7943+ζ7941 ζ7952+ζ7916+ζ7911 ζ7932+ζ7925+ζ7922 complex faithful ρ7 3 0 0 ζ7932+ζ7925+ζ7922 ζ7969+ζ797+ζ793 ζ7968+ζ7963+ζ7927 ζ7964+ζ7950+ζ7944 ζ7959+ζ7914+ζ796 ζ7975+ζ7966+ζ7917 ζ7957+ζ7954+ζ7947 ζ7939+ζ7928+ζ7912 ζ7949+ζ7921+ζ799 ζ7946+ζ7931+ζ792 ζ7976+ζ7972+ζ7910 ζ7971+ζ7953+ζ7934 ζ7935+ζ7929+ζ7915 ζ7978+ζ7956+ζ7924 ζ7942+ζ7919+ζ7918 ζ7967+ζ7951+ζ7940 ζ7962+ζ7913+ζ794 ζ7938+ζ7936+ζ795 ζ7973+ζ7965+ζ7920 ζ7945+ζ7926+ζ798 ζ7970+ζ7958+ζ7930 ζ7952+ζ7916+ζ7911 ζ7977+ζ7948+ζ7933 ζ7955+ζ7923+ζ79 ζ7961+ζ7960+ζ7937 ζ7974+ζ7943+ζ7941 complex faithful ρ8 3 0 0 ζ7973+ζ7965+ζ7920 ζ7971+ζ7953+ζ7934 ζ7969+ζ797+ζ793 ζ7967+ζ7951+ζ7940 ζ7968+ζ7963+ζ7927 ζ7961+ζ7960+ζ7937 ζ7959+ζ7914+ζ796 ζ7957+ζ7954+ζ7947 ζ7955+ζ7923+ζ79 ζ7949+ζ7921+ζ799 ζ7945+ζ7926+ζ798 ζ7974+ζ7943+ζ7941 ζ7939+ζ7928+ζ7912 ζ7935+ζ7929+ζ7915 ζ7946+ζ7931+ζ792 ζ7932+ζ7925+ζ7922 ζ7942+ζ7919+ζ7918 ζ7962+ζ7913+ζ794 ζ7952+ζ7916+ζ7911 ζ7938+ζ7936+ζ795 ζ7978+ζ7956+ζ7924 ζ7976+ζ7972+ζ7910 ζ7970+ζ7958+ζ7930 ζ7964+ζ7950+ζ7944 ζ7977+ζ7948+ζ7933 ζ7975+ζ7966+ζ7917 complex faithful ρ9 3 0 0 ζ7945+ζ7926+ζ798 ζ7961+ζ7960+ζ7937 ζ7975+ζ7966+ζ7917 ζ7952+ζ7916+ζ7911 ζ7974+ζ7943+ζ7941 ζ7978+ζ7956+ζ7924 ζ7971+ζ7953+ζ7934 ζ7969+ζ797+ζ793 ζ7932+ζ7925+ζ7922 ζ7967+ζ7951+ζ7940 ζ7942+ζ7919+ζ7918 ζ7977+ζ7948+ζ7933 ζ7968+ζ7963+ζ7927 ζ7959+ζ7914+ζ796 ζ7964+ζ7950+ζ7944 ζ7976+ζ7972+ζ7910 ζ7955+ζ7923+ζ79 ζ7949+ζ7921+ζ799 ζ7938+ζ7936+ζ795 ζ7946+ζ7931+ζ792 ζ7957+ζ7954+ζ7947 ζ7962+ζ7913+ζ794 ζ7939+ζ7928+ζ7912 ζ7973+ζ7965+ζ7920 ζ7935+ζ7929+ζ7915 ζ7970+ζ7958+ζ7930 complex faithful ρ10 3 0 0 ζ7957+ζ7954+ζ7947 ζ7976+ζ7972+ζ7910 ζ7952+ζ7916+ζ7911 ζ7935+ζ7929+ζ7915 ζ7973+ζ7965+ζ7920 ζ7962+ζ7913+ζ794 ζ7932+ζ7925+ζ7922 ζ7967+ζ7951+ζ7940 ζ7970+ζ7958+ζ7930 ζ7977+ζ7948+ζ7933 ζ7969+ζ797+ζ793 ζ7945+ζ7926+ζ798 ζ7964+ζ7950+ζ7944 ζ7955+ζ7923+ζ79 ζ7961+ζ7960+ζ7937 ζ7939+ζ7928+ζ7912 ζ7975+ζ7966+ζ7917 ζ7974+ζ7943+ζ7941 ζ7959+ζ7914+ζ796 ζ7971+ζ7953+ζ7934 ζ7949+ζ7921+ζ799 ζ7968+ζ7963+ζ7927 ζ7946+ζ7931+ζ792 ζ7978+ζ7956+ζ7924 ζ7942+ζ7919+ζ7918 ζ7938+ζ7936+ζ795 complex faithful ρ11 3 0 0 ζ7975+ζ7966+ζ7917 ζ7949+ζ7921+ζ799 ζ7946+ζ7931+ζ792 ζ7971+ζ7953+ζ7934 ζ7942+ζ7919+ζ7918 ζ7967+ζ7951+ζ7940 ζ7962+ζ7913+ζ794 ζ7938+ζ7936+ζ795 ζ7968+ζ7963+ζ7927 ζ7959+ζ7914+ζ796 ζ7970+ζ7958+ζ7930 ζ7955+ζ7923+ζ79 ζ7945+ζ7926+ζ798 ζ7976+ζ7972+ζ7910 ζ7957+ζ7954+ζ7947 ζ7974+ζ7943+ζ7941 ζ7939+ζ7928+ζ7912 ζ7935+ζ7929+ζ7915 ζ7961+ζ7960+ζ7937 ζ7978+ζ7956+ζ7924 ζ7952+ζ7916+ζ7911 ζ7977+ζ7948+ζ7933 ζ7973+ζ7965+ζ7920 ζ7969+ζ797+ζ793 ζ7932+ζ7925+ζ7922 ζ7964+ζ7950+ζ7944 complex faithful ρ12 3 0 0 ζ7935+ζ7929+ζ7915 ζ7973+ζ7965+ζ7920 ζ7932+ζ7925+ζ7922 ζ7970+ζ7958+ζ7930 ζ7967+ζ7951+ζ7940 ζ7945+ζ7926+ζ798 ζ7964+ζ7950+ζ7944 ζ7955+ζ7923+ζ79 ζ7961+ζ7960+ζ7937 ζ7975+ζ7966+ζ7917 ζ7959+ζ7914+ζ796 ζ7952+ζ7916+ζ7911 ζ7949+ζ7921+ζ799 ζ7946+ζ7931+ζ792 ζ7974+ζ7943+ζ7941 ζ7978+ζ7956+ζ7924 ζ7971+ζ7953+ζ7934 ζ7969+ζ797+ζ793 ζ7939+ζ7928+ζ7912 ζ7968+ζ7963+ζ7927 ζ7942+ζ7919+ζ7918 ζ7957+ζ7954+ζ7947 ζ7962+ζ7913+ζ794 ζ7977+ζ7948+ζ7933 ζ7938+ζ7936+ζ795 ζ7976+ζ7972+ζ7910 complex faithful ρ13 3 0 0 ζ7955+ζ7923+ζ79 ζ7957+ζ7954+ζ7947 ζ7939+ζ7928+ζ7912 ζ7946+ζ7931+ζ792 ζ7935+ζ7929+ζ7915 ζ7969+ζ797+ζ793 ζ7978+ζ7956+ζ7924 ζ7970+ζ7958+ζ7930 ζ7962+ζ7913+ζ794 ζ7938+ζ7936+ζ795 ζ7932+ζ7925+ζ7922 ζ7959+ζ7914+ζ796 ζ7977+ζ7948+ζ7933 ζ7961+ζ7960+ζ7937 ζ7945+ζ7926+ζ798 ζ7949+ζ7921+ζ799 ζ7976+ζ7972+ζ7910 ζ7952+ζ7916+ζ7911 ζ7964+ζ7950+ζ7944 ζ7973+ζ7965+ζ7920 ζ7975+ζ7966+ζ7917 ζ7967+ζ7951+ζ7940 ζ7974+ζ7943+ζ7941 ζ7942+ζ7919+ζ7918 ζ7971+ζ7953+ζ7934 ζ7968+ζ7963+ζ7927 complex faithful ρ14 3 0 0 ζ7967+ζ7951+ζ7940 ζ7968+ζ7963+ζ7927 ζ7959+ζ7914+ζ796 ζ7955+ζ7923+ζ79 ζ7957+ζ7954+ζ7947 ζ7974+ζ7943+ζ7941 ζ7939+ζ7928+ζ7912 ζ7935+ζ7929+ζ7915 ζ7946+ζ7931+ζ792 ζ7942+ζ7919+ζ7918 ζ7952+ζ7916+ζ7911 ζ7969+ζ797+ζ793 ζ7978+ζ7956+ζ7924 ζ7970+ζ7958+ζ7930 ζ7962+ζ7913+ζ794 ζ7964+ζ7950+ζ7944 ζ7938+ζ7936+ζ795 ζ7945+ζ7926+ζ798 ζ7932+ζ7925+ζ7922 ζ7976+ζ7972+ζ7910 ζ7977+ζ7948+ζ7933 ζ7973+ζ7965+ζ7920 ζ7961+ζ7960+ζ7937 ζ7949+ζ7921+ζ799 ζ7975+ζ7966+ζ7917 ζ7971+ζ7953+ζ7934 complex faithful ρ15 3 0 0 ζ7969+ζ797+ζ793 ζ7962+ζ7913+ζ794 ζ7938+ζ7936+ζ795 ζ7959+ζ7914+ζ796 ζ7945+ζ7926+ζ798 ζ7949+ζ7921+ζ799 ζ7976+ζ7972+ζ7910 ζ7952+ζ7916+ζ7911 ζ7939+ζ7928+ζ7912 ζ7935+ζ7929+ζ7915 ζ7975+ζ7966+ζ7917 ζ7942+ζ7919+ζ7918 ζ7973+ζ7965+ζ7920 ζ7932+ζ7925+ζ7922 ζ7978+ζ7956+ζ7924 ζ7968+ζ7963+ζ7927 ζ7970+ζ7958+ζ7930 ζ7977+ζ7948+ζ7933 ζ7971+ζ7953+ζ7934 ζ7961+ζ7960+ζ7937 ζ7967+ζ7951+ζ7940 ζ7974+ζ7943+ζ7941 ζ7964+ζ7950+ζ7944 ζ7957+ζ7954+ζ7947 ζ7955+ζ7923+ζ79 ζ7946+ζ7931+ζ792 complex faithful ρ16 3 0 0 ζ7938+ζ7936+ζ795 ζ7977+ζ7948+ζ7933 ζ7961+ζ7960+ζ7937 ζ7976+ζ7972+ζ7910 ζ7975+ζ7966+ζ7917 ζ7935+ζ7929+ζ7915 ζ7974+ζ7943+ζ7941 ζ7971+ζ7953+ζ7934 ζ7973+ζ7965+ζ7920 ζ7932+ζ7925+ζ7922 ζ7946+ζ7931+ζ792 ζ7970+ζ7958+ζ7930 ζ7969+ζ797+ζ793 ζ7968+ζ7963+ζ7927 ζ7967+ζ7951+ζ7940 ζ7945+ζ7926+ζ798 ζ7964+ζ7950+ζ7944 ζ7955+ζ7923+ζ79 ζ7962+ζ7913+ζ794 ζ7949+ζ7921+ζ799 ζ7959+ζ7914+ζ796 ζ7942+ζ7919+ζ7918 ζ7957+ζ7954+ζ7947 ζ7952+ζ7916+ζ7911 ζ7939+ζ7928+ζ7912 ζ7978+ζ7956+ζ7924 complex faithful ρ17 3 0 0 ζ7968+ζ7963+ζ7927 ζ7938+ζ7936+ζ795 ζ7945+ζ7926+ζ798 ζ7957+ζ7954+ζ7947 ζ7976+ζ7972+ζ7910 ζ7946+ζ7931+ζ792 ζ7952+ζ7916+ζ7911 ζ7973+ζ7965+ζ7920 ζ7935+ζ7929+ζ7915 ζ7978+ζ7956+ζ7924 ζ7974+ζ7943+ζ7941 ζ7962+ζ7913+ζ794 ζ7932+ζ7925+ζ7922 ζ7967+ζ7951+ζ7940 ζ7970+ζ7958+ζ7930 ζ7959+ζ7914+ζ796 ζ7977+ζ7948+ζ7933 ζ7961+ζ7960+ζ7937 ζ7969+ζ797+ζ793 ζ7975+ζ7966+ζ7917 ζ7964+ζ7950+ζ7944 ζ7971+ζ7953+ζ7934 ζ7955+ζ7923+ζ79 ζ7939+ζ7928+ζ7912 ζ7949+ζ7921+ζ799 ζ7942+ζ7919+ζ7918 complex faithful ρ18 3 0 0 ζ7971+ζ7953+ζ7934 ζ7942+ζ7919+ζ7918 ζ7962+ζ7913+ζ794 ζ7968+ζ7963+ζ7927 ζ7938+ζ7936+ζ795 ζ7955+ζ7923+ζ79 ζ7945+ζ7926+ζ798 ζ7976+ζ7972+ζ7910 ζ7957+ζ7954+ζ7947 ζ7939+ζ7928+ζ7912 ζ7961+ζ7960+ζ7937 ζ7946+ζ7931+ζ792 ζ7952+ζ7916+ζ7911 ζ7973+ζ7965+ζ7920 ζ7935+ζ7929+ζ7915 ζ7969+ζ797+ζ793 ζ7978+ζ7956+ζ7924 ζ7970+ζ7958+ζ7930 ζ7974+ζ7943+ζ7941 ζ7977+ζ7948+ζ7933 ζ7932+ζ7925+ζ7922 ζ7975+ζ7966+ζ7917 ζ7967+ζ7951+ζ7940 ζ7959+ζ7914+ζ796 ζ7964+ζ7950+ζ7944 ζ7949+ζ7921+ζ799 complex faithful ρ19 3 0 0 ζ7939+ζ7928+ζ7912 ζ7952+ζ7916+ζ7911 ζ7973+ζ7965+ζ7920 ζ7978+ζ7956+ζ7924 ζ7932+ζ7925+ζ7922 ζ7938+ζ7936+ζ795 ζ7967+ζ7951+ζ7940 ζ7964+ζ7950+ζ7944 ζ7977+ζ7948+ζ7933 ζ7961+ζ7960+ζ7937 ζ7968+ζ7963+ζ7927 ζ7976+ζ7972+ζ7910 ζ7955+ζ7923+ζ79 ζ7949+ζ7921+ζ799 ζ7975+ζ7966+ζ7917 ζ7935+ζ7929+ζ7915 ζ7974+ζ7943+ζ7941 ζ7971+ζ7953+ζ7934 ζ7957+ζ7954+ζ7947 ζ7969+ζ797+ζ793 ζ7946+ζ7931+ζ792 ζ7959+ζ7914+ζ796 ζ7942+ζ7919+ζ7918 ζ7970+ζ7958+ζ7930 ζ7962+ζ7913+ζ794 ζ7945+ζ7926+ζ798 complex faithful ρ20 3 0 0 ζ7942+ζ7919+ζ7918 ζ7978+ζ7956+ζ7924 ζ7970+ζ7958+ζ7930 ζ7938+ζ7936+ζ795 ζ7977+ζ7948+ζ7933 ζ7957+ζ7954+ζ7947 ζ7961+ζ7960+ζ7937 ζ7975+ζ7966+ζ7917 ζ7976+ζ7972+ζ7910 ζ7952+ζ7916+ζ7911 ζ7955+ζ7923+ζ79 ζ7935+ζ7929+ζ7915 ζ7974+ζ7943+ζ7941 ζ7971+ζ7953+ζ7934 ζ7973+ζ7965+ζ7920 ζ7962+ζ7913+ζ794 ζ7932+ζ7925+ζ7922 ζ7967+ζ7951+ζ7940 ζ7946+ζ7931+ζ792 ζ7964+ζ7950+ζ7944 ζ7969+ζ797+ζ793 ζ7949+ζ7921+ζ799 ζ7968+ζ7963+ζ7927 ζ7945+ζ7926+ζ798 ζ7959+ζ7914+ζ796 ζ7939+ζ7928+ζ7912 complex faithful ρ21 3 0 0 ζ7959+ζ7914+ζ796 ζ7945+ζ7926+ζ798 ζ7976+ζ7972+ζ7910 ζ7939+ζ7928+ζ7912 ζ7952+ζ7916+ζ7911 ζ7942+ζ7919+ζ7918 ζ7973+ζ7965+ζ7920 ζ7932+ζ7925+ζ7922 ζ7978+ζ7956+ζ7924 ζ7970+ζ7958+ζ7930 ζ7971+ζ7953+ζ7934 ζ7938+ζ7936+ζ795 ζ7967+ζ7951+ζ7940 ζ7964+ζ7950+ζ7944 ζ7977+ζ7948+ζ7933 ζ7957+ζ7954+ζ7947 ζ7961+ζ7960+ζ7937 ζ7975+ζ7966+ζ7917 ζ7968+ζ7963+ζ7927 ζ7974+ζ7943+ζ7941 ζ7955+ζ7923+ζ79 ζ7969+ζ797+ζ793 ζ7949+ζ7921+ζ799 ζ7935+ζ7929+ζ7915 ζ7946+ζ7931+ζ792 ζ7962+ζ7913+ζ794 complex faithful ρ22 3 0 0 ζ7949+ζ7921+ζ799 ζ7939+ζ7928+ζ7912 ζ7935+ζ7929+ζ7915 ζ7942+ζ7919+ζ7918 ζ7978+ζ7956+ζ7924 ζ7968+ζ7963+ζ7927 ζ7970+ζ7958+ζ7930 ζ7977+ζ7948+ζ7933 ζ7938+ζ7936+ζ795 ζ7945+ζ7926+ζ798 ζ7967+ζ7951+ζ7940 ζ7957+ζ7954+ζ7947 ζ7961+ζ7960+ζ7937 ζ7975+ζ7966+ζ7917 ζ7976+ζ7972+ζ7910 ζ7946+ζ7931+ζ792 ζ7952+ζ7916+ζ7911 ζ7973+ζ7965+ζ7920 ζ7955+ζ7923+ζ79 ζ7932+ζ7925+ζ7922 ζ7974+ζ7943+ζ7941 ζ7964+ζ7950+ζ7944 ζ7971+ζ7953+ζ7934 ζ7962+ζ7913+ζ794 ζ7969+ζ797+ζ793 ζ7959+ζ7914+ζ796 complex faithful ρ23 3 0 0 ζ7962+ζ7913+ζ794 ζ7970+ζ7958+ζ7930 ζ7977+ζ7948+ζ7933 ζ7945+ζ7926+ζ798 ζ7961+ζ7960+ζ7937 ζ7939+ζ7928+ζ7912 ζ7975+ζ7966+ζ7917 ζ7974+ζ7943+ζ7941 ζ7952+ζ7916+ζ7911 ζ7973+ζ7965+ζ7920 ζ7949+ζ7921+ζ799 ζ7978+ζ7956+ζ7924 ζ7971+ζ7953+ζ7934 ζ7969+ζ797+ζ793 ζ7932+ζ7925+ζ7922 ζ7938+ζ7936+ζ795 ζ7967+ζ7951+ζ7940 ζ7964+ζ7950+ζ7944 ζ7942+ζ7919+ζ7918 ζ7955+ζ7923+ζ79 ζ7968+ζ7963+ζ7927 ζ7946+ζ7931+ζ792 ζ7959+ζ7914+ζ796 ζ7976+ζ7972+ζ7910 ζ7957+ζ7954+ζ7947 ζ7935+ζ7929+ζ7915 complex faithful ρ24 3 0 0 ζ7952+ζ7916+ζ7911 ζ7974+ζ7943+ζ7941 ζ7971+ζ7953+ζ7934 ζ7932+ζ7925+ζ7922 ζ7969+ζ797+ζ793 ζ7977+ζ7948+ζ7933 ζ7968+ζ7963+ζ7927 ζ7959+ζ7914+ζ796 ζ7964+ζ7950+ζ7944 ζ7955+ζ7923+ζ79 ζ7938+ζ7936+ζ795 ζ7975+ζ7966+ζ7917 ζ7957+ζ7954+ζ7947 ζ7939+ζ7928+ζ7912 ζ7949+ζ7921+ζ799 ζ7973+ζ7965+ζ7920 ζ7946+ζ7931+ζ792 ζ7942+ζ7919+ζ7918 ζ7976+ζ7972+ζ7910 ζ7962+ζ7913+ζ794 ζ7935+ζ7929+ζ7915 ζ7945+ζ7926+ζ798 ζ7978+ζ7956+ζ7924 ζ7967+ζ7951+ζ7940 ζ7970+ζ7958+ζ7930 ζ7961+ζ7960+ζ7937 complex faithful ρ25 3 0 0 ζ7978+ζ7956+ζ7924 ζ7932+ζ7925+ζ7922 ζ7967+ζ7951+ζ7940 ζ7977+ζ7948+ζ7933 ζ7964+ζ7950+ζ7944 ζ7976+ζ7972+ζ7910 ζ7955+ζ7923+ζ79 ζ7949+ζ7921+ζ799 ζ7975+ζ7966+ζ7917 ζ7974+ζ7943+ζ7941 ζ7957+ζ7954+ζ7947 ζ7973+ζ7965+ζ7920 ζ7946+ζ7931+ζ792 ζ7942+ζ7919+ζ7918 ζ7971+ζ7953+ζ7934 ζ7970+ζ7958+ζ7930 ζ7969+ζ797+ζ793 ζ7968+ζ7963+ζ7927 ζ7935+ζ7929+ζ7915 ζ7959+ζ7914+ζ796 ζ7962+ζ7913+ζ794 ζ7939+ζ7928+ζ7912 ζ7938+ζ7936+ζ795 ζ7961+ζ7960+ζ7937 ζ7945+ζ7926+ζ798 ζ7952+ζ7916+ζ7911 complex faithful ρ26 3 0 0 ζ7976+ζ7972+ζ7910 ζ7975+ζ7966+ζ7917 ζ7974+ζ7943+ζ7941 ζ7973+ζ7965+ζ7920 ζ7971+ζ7953+ζ7934 ζ7970+ζ7958+ζ7930 ζ7969+ζ797+ζ793 ζ7968+ζ7963+ζ7927 ζ7967+ζ7951+ζ7940 ζ7964+ζ7950+ζ7944 ζ7962+ζ7913+ζ794 ζ7961+ζ7960+ζ7937 ζ7959+ζ7914+ζ796 ζ7957+ζ7954+ζ7947 ζ7955+ζ7923+ζ79 ζ7952+ζ7916+ζ7911 ζ7949+ζ7921+ζ799 ζ7946+ζ7931+ζ792 ζ7945+ζ7926+ζ798 ζ7942+ζ7919+ζ7918 ζ7939+ζ7928+ζ7912 ζ7938+ζ7936+ζ795 ζ7935+ζ7929+ζ7915 ζ7932+ζ7925+ζ7922 ζ7978+ζ7956+ζ7924 ζ7977+ζ7948+ζ7933 complex faithful ρ27 3 0 0 ζ7946+ζ7931+ζ792 ζ7935+ζ7929+ζ7915 ζ7978+ζ7956+ζ7924 ζ7962+ζ7913+ζ794 ζ7970+ζ7958+ζ7930 ζ7959+ζ7914+ζ796 ζ7977+ζ7948+ζ7933 ζ7961+ζ7960+ζ7937 ζ7945+ζ7926+ζ798 ζ7976+ζ7972+ζ7910 ζ7964+ζ7950+ζ7944 ζ7939+ζ7928+ζ7912 ζ7975+ζ7966+ζ7917 ζ7974+ζ7943+ζ7941 ζ7952+ζ7916+ζ7911 ζ7942+ζ7919+ζ7918 ζ7973+ζ7965+ζ7920 ζ7932+ζ7925+ζ7922 ζ7949+ζ7921+ζ799 ζ7967+ζ7951+ζ7940 ζ7971+ζ7953+ζ7934 ζ7955+ζ7923+ζ79 ζ7969+ζ797+ζ793 ζ7938+ζ7936+ζ795 ζ7968+ζ7963+ζ7927 ζ7957+ζ7954+ζ7947 complex faithful ρ28 3 0 0 ζ7970+ζ7958+ζ7930 ζ7967+ζ7951+ζ7940 ζ7964+ζ7950+ζ7944 ζ7961+ζ7960+ζ7937 ζ7955+ζ7923+ζ79 ζ7952+ζ7916+ζ7911 ζ7949+ζ7921+ζ799 ζ7946+ζ7931+ζ792 ζ7974+ζ7943+ζ7941 ζ7971+ζ7953+ζ7934 ζ7939+ζ7928+ζ7912 ζ7932+ζ7925+ζ7922 ζ7942+ζ7919+ζ7918 ζ7962+ζ7913+ζ794 ζ7969+ζ797+ζ793 ζ7977+ζ7948+ζ7933 ζ7968+ζ7963+ζ7927 ζ7959+ζ7914+ζ796 ζ7978+ζ7956+ζ7924 ζ7957+ζ7954+ζ7947 ζ7938+ζ7936+ζ795 ζ7935+ζ7929+ζ7915 ζ7945+ζ7926+ζ798 ζ7975+ζ7966+ζ7917 ζ7976+ζ7972+ζ7910 ζ7973+ζ7965+ζ7920 complex faithful ρ29 3 0 0 ζ7961+ζ7960+ζ7937 ζ7955+ζ7923+ζ79 ζ7949+ζ7921+ζ799 ζ7974+ζ7943+ζ7941 ζ7946+ζ7931+ζ792 ζ7932+ζ7925+ζ7922 ζ7942+ζ7919+ζ7918 ζ7962+ζ7913+ζ794 ζ7969+ζ797+ζ793 ζ7968+ζ7963+ζ7927 ζ7978+ζ7956+ζ7924 ζ7964+ζ7950+ζ7944 ζ7938+ζ7936+ζ795 ζ7945+ζ7926+ζ798 ζ7959+ζ7914+ζ796 ζ7975+ζ7966+ζ7917 ζ7957+ζ7954+ζ7947 ζ7939+ζ7928+ζ7912 ζ7977+ζ7948+ζ7933 ζ7935+ζ7929+ζ7915 ζ7976+ζ7972+ζ7910 ζ7970+ζ7958+ζ7930 ζ7952+ζ7916+ζ7911 ζ7971+ζ7953+ζ7934 ζ7973+ζ7965+ζ7920 ζ7967+ζ7951+ζ7940 complex faithful

Smallest permutation representation of C79⋊C3
On 79 points: primitive
Generators in S79
```(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 75 76 77 78 79)
(2 24 56)(3 47 32)(4 70 8)(5 14 63)(6 37 39)(7 60 15)(9 27 46)(10 50 22)(11 73 77)(12 17 53)(13 40 29)(16 30 36)(18 76 67)(19 20 43)(21 66 74)(23 33 26)(25 79 57)(28 69 64)(31 59 71)(34 49 78)(35 72 54)(38 62 61)(41 52 68)(42 75 44)(45 65 51)(48 55 58)```

`G:=sub<Sym(79)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79), (2,24,56)(3,47,32)(4,70,8)(5,14,63)(6,37,39)(7,60,15)(9,27,46)(10,50,22)(11,73,77)(12,17,53)(13,40,29)(16,30,36)(18,76,67)(19,20,43)(21,66,74)(23,33,26)(25,79,57)(28,69,64)(31,59,71)(34,49,78)(35,72,54)(38,62,61)(41,52,68)(42,75,44)(45,65,51)(48,55,58)>;`

`G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79), (2,24,56)(3,47,32)(4,70,8)(5,14,63)(6,37,39)(7,60,15)(9,27,46)(10,50,22)(11,73,77)(12,17,53)(13,40,29)(16,30,36)(18,76,67)(19,20,43)(21,66,74)(23,33,26)(25,79,57)(28,69,64)(31,59,71)(34,49,78)(35,72,54)(38,62,61)(41,52,68)(42,75,44)(45,65,51)(48,55,58) );`

`G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79)], [(2,24,56),(3,47,32),(4,70,8),(5,14,63),(6,37,39),(7,60,15),(9,27,46),(10,50,22),(11,73,77),(12,17,53),(13,40,29),(16,30,36),(18,76,67),(19,20,43),(21,66,74),(23,33,26),(25,79,57),(28,69,64),(31,59,71),(34,49,78),(35,72,54),(38,62,61),(41,52,68),(42,75,44),(45,65,51),(48,55,58)]])`

C79⋊C3 is a maximal subgroup of   C79⋊C6

Matrix representation of C79⋊C3 in GL3(𝔽1423) generated by

 0 1 0 0 0 1 1 490 104
,
 1 0 0 859 1374 970 630 1246 48
`G:=sub<GL(3,GF(1423))| [0,0,1,1,0,490,0,1,104],[1,859,630,0,1374,1246,0,970,48] >;`

C79⋊C3 in GAP, Magma, Sage, TeX

`C_{79}\rtimes C_3`
`% in TeX`

`G:=Group("C79:C3");`
`// GroupNames label`

`G:=SmallGroup(237,1);`
`// by ID`

`G=gap.SmallGroup(237,1);`
`# by ID`

`G:=PCGroup([2,-3,-79,277]);`
`// Polycyclic`

`G:=Group<a,b|a^79=b^3=1,b*a*b^-1=a^55>;`
`// generators/relations`

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