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C₄²×C₅×C₈×C₉ #72184997

order	5760
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2359296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

abelian	C₄²×C₅×C₈×C₉
multiplicative	(ℤ/7585)ˣ, (ℤ/15170)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₅×C₉×C₁₆, C₄×C₅×C₈²×C₉, C₂×C₄²×C₅×C₈×C₉, …
maximal normal subgroup of	C₄²×C₅×C₉×C₁₆, C₄×C₅×C₈²×C₉, C₂×C₄²×C₅×C₈×C₉, …
maximal quotient of	C₄²×C₅×C₉×C₁₆, C₄×C₅×C₈²×C₉, C₂×C₄²×C₅×C₈×C₉, …
automorphism group of	C₅×C₃₇×C₄₁
outer automorphism group of	C₅×C₃₇×C₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.