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C₃²×C₈×C₉×C₁₆ #72188993

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 47775744
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₈

Aliases

C₃²×C₈×C₉×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₈	C₂²×C₃³
socle, prime radical	C₂²×C₃³	C₃×C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

2600 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×C₈×C₉×C₃₂, C₃²×C₉×C₁₆², C₂×C₃²×C₈×C₉×C₁₆, …
maximal normal subgroup of	C₃²×C₈×C₉×C₃₂, C₃²×C₉×C₁₆², C₂×C₃²×C₈×C₉×C₁₆, …
maximal quotient of	C₃²×C₈×C₉×C₃₂, C₃²×C₉×C₁₆², C₂×C₃²×C₈×C₉×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.