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C₃²×C₄²×C₂₅ #72183265

order	3600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 92160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

C₃²×C₄²×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₅	C₂²×C₃²×C₅
socle, prime radical	C₂²×C₃²×C₅	C₂²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

270 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₈×C₂₅, C₂×C₃²×C₄²×C₂₅, C₃×C₄²×C₉×C₂₅, …
maximal normal subgroup of	C₃²×C₄×C₈×C₂₅, C₂×C₃²×C₄²×C₂₅, C₃×C₄²×C₉×C₂₅, …
maximal quotient of	C₃²×C₄×C₈×C₂₅, C₂×C₃²×C₄²×C₂₅, C₃×C₄²×C₉×C₂₅, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.