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C₃²×C₄²×C₈×C₉ #72189013

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2293235712
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄³

Aliases

C₃²×C₄²×C₈×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₂²×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

10200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄²×C₉×C₁₆, C₃²×C₄×C₈²×C₉, C₂×C₃²×C₄²×C₈×C₉, …
maximal normal subgroup of	C₃²×C₄²×C₉×C₁₆, C₃²×C₄×C₈²×C₉, C₂×C₃²×C₄²×C₈×C₉, …
maximal quotient of	C₃²×C₄²×C₉×C₁₆, C₃²×C₄×C₈²×C₉, C₂×C₃²×C₄²×C₈×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.