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C₂²×C₃²×C₈×C₉ #72182479

order	2592
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8957952
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂²×C₃²×C₈×C₉
multiplicative	(ℤ/4599)ˣ, (ℤ/9198)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₉×C₁₆, C₂×C₃²×C₄×C₈×C₉, C₂³×C₃²×C₈×C₉, …
maximal normal subgroup of	C₂²×C₃²×C₉×C₁₆, C₂×C₃²×C₄×C₈×C₉, C₂³×C₃²×C₈×C₉, …
maximal quotient of	C₂²×C₃²×C₉×C₁₆, C₂×C₃²×C₄×C₈×C₉, C₂³×C₃²×C₈×C₉, …
automorphism group of	C₇×C₉×C₇₃, C₂×C₇×C₉×C₇₃
outer automorphism group of	C₇×C₉×C₇₃, C₂×C₇×C₉×C₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.