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C₃³×C₅²×C₁₆ #72189337

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 43130880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₅

Aliases

C₃³×C₅²×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃³×C₅²
socle, prime radical	C₂×C₃³×C₅²	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃³×C₅²×C₃₂, C₂×C₃³×C₅²×C₁₆, C₃²×C₅²×C₉×C₁₆, …
maximal normal subgroup of	C₃³×C₅²×C₃₂, C₂×C₃³×C₅²×C₁₆, C₃²×C₅²×C₉×C₁₆, …
maximal quotient of	C₃³×C₅²×C₃₂, C₂×C₃³×C₅²×C₁₆, C₃²×C₅²×C₉×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.