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C₄×C₂₇×C₈₉ #72188338

order	9612
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₈×C₉×C₁₁ (order 3168) · Inn(G) = C₁ · Out(G) = C₂²×C₈×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₆₁₂
abelian	C₄×C₂₇×C₈₉
multiplicative	(ℤ/9613)ˣ, (ℤ/19226)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃×C₈₉
socle, prime radical	C₂×C₃×C₈₉	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9612 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₆₁₂, D₁₉₂₂₄
maximal subgroup of	C₈×C₂₇×C₈₉, C₂×C₄×C₂₇×C₈₉, C₄×C₈₁×C₈₉, …
maximal normal subgroup of	C₈×C₂₇×C₈₉, C₂×C₄×C₂₇×C₈₉, C₄×C₈₁×C₈₉, …
maximal quotient of	C₈×C₂₇×C₈₉, C₂×C₄×C₂₇×C₈₉, C₄×C₈₁×C₈₉, …
automorphism group of	C₉₆₁₃
outer automorphism group of	C₉₆₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.