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C₃×C₈×C₃₈₉ #72188126

order	9336
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄×C₉₇ (order 3104) · Inn(G) = C₁ · Out(G) = C₂³×C₄×C₉₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₃₃₆
abelian	C₃×C₈×C₃₈₉
multiplicative	(ℤ/9337)ˣ, (ℤ/18674)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₃₈₉
socle, prime radical	C₂×C₃×C₃₈₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9336 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₃₃₆, D₁₈₆₇₂
maximal subgroup of	C₃×C₁₆×C₃₈₉, C₂×C₃×C₈×C₃₈₉, C₈×C₉×C₃₈₉, …
maximal normal subgroup of	C₃×C₁₆×C₃₈₉, C₂×C₃×C₈×C₃₈₉, C₈×C₉×C₃₈₉, …
maximal quotient of	C₃×C₁₆×C₃₈₉, C₂×C₃×C₈×C₃₈₉, C₈×C₉×C₃₈₉, …
automorphism group of	C₉₃₃₇
outer automorphism group of	C₉₃₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.