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C₃³×C₄²×C₂₅ #72189348

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 21565440
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄

Aliases

C₃³×C₄²×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₅	C₂²×C₃³×C₅
socle, prime radical	C₂²×C₃³×C₅	C₂²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

1260 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×C₄×C₈×C₂₅, C₂×C₃³×C₄²×C₂₅, C₃²×C₄²×C₉×C₂₅, …
maximal normal subgroup of	C₃³×C₄×C₈×C₂₅, C₂×C₃³×C₄²×C₂₅, C₃²×C₄²×C₉×C₂₅, …
maximal quotient of	C₃³×C₄×C₈×C₂₅, C₂×C₃³×C₄²×C₂₅, C₃²×C₄²×C₉×C₂₅, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.