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C₂×C₄×C₅×C₈₉ #72183207

order	3560
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2816
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₅×C₈₉
multiplicative	(ℤ/4475)ˣ, (ℤ/8950)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅×C₈₉
socle, prime radical	C₂²×C₅×C₈₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₅×C₈₉, C₂×C₅×C₈×C₈₉, C₂²×C₄×C₅×C₈₉, …
maximal normal subgroup of	C₄²×C₅×C₈₉, C₂×C₅×C₈×C₈₉, C₂²×C₄×C₅×C₈₉, …
maximal quotient of	C₄²×C₅×C₈₉, C₂×C₅×C₈×C₈₉, C₂²×C₄×C₅×C₈₉, …
automorphism group of	C₂₅×C₁₇₉, C₂×C₂₅×C₁₇₉
outer automorphism group of	C₂₅×C₁₇₉, C₂×C₂₅×C₁₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.