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C₄×C₉×C₁₃×C₁₉ #22580098

order	8892
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₄×C₉ (order 2592) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₄×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₈₉₂
abelian	C₄×C₉×C₁₃×C₁₉
multiplicative	(ℤ/8893)ˣ, (ℤ/17786)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₃	C₂×C₃×C₁₃×C₁₉
socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8892 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₈₉₂, D₁₇₇₈₄
maximal subgroup of	C₈×C₉×C₁₃×C₁₉, C₂×C₄×C₉×C₁₃×C₁₉, C₄×C₁₃×C₁₉×C₂₇, …
maximal normal subgroup of	C₈×C₉×C₁₃×C₁₉, C₂×C₄×C₉×C₁₃×C₁₉, C₄×C₁₃×C₁₉×C₂₇, …
maximal quotient of	C₈×C₉×C₁₃×C₁₉, C₂×C₄×C₉×C₁₃×C₁₉, C₄×C₁₃×C₁₉×C₂₇, …
automorphism group of	C₈₈₉₃
outer automorphism group of	C₈₈₉₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 1);