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C₂×C₅×C₈×C₈₉ #72186169

order	7120
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5632
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₅×C₈×C₈₉
multiplicative	(ℤ/7339)ˣ, (ℤ/14678)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₅×C₈₉
socle, prime radical	C₂²×C₅×C₈₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₁₆×C₈₉, C₄×C₅×C₈×C₈₉, C₂²×C₅×C₈×C₈₉, …
maximal normal subgroup of	C₂×C₅×C₁₆×C₈₉, C₄×C₅×C₈×C₈₉, C₂²×C₅×C₈×C₈₉, …
maximal quotient of	C₂×C₅×C₁₆×C₈₉, C₄×C₅×C₈×C₈₉, C₂²×C₅×C₈×C₈₉, …
automorphism group of	C₄₁×C₁₇₉
outer automorphism group of	C₄₁×C₁₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.