Finite Group Databasebeta

← Prev (#72183265) Next (#72183267) →

C₃²×C₄²×C₅² #72183266

order	3600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2211840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄×C₅

Aliases

C₃²×C₄²×C₅²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃²×C₅²
socle, prime radical	C₂²×C₃²×C₅²	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

720 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×C₅²×C₈, C₂×C₃²×C₄²×C₅², C₃×C₄²×C₅²×C₉, …
maximal normal subgroup of	C₃²×C₄×C₅²×C₈, C₂×C₃²×C₄²×C₅², C₃×C₄²×C₅²×C₉, …
maximal quotient of	C₃²×C₄×C₅²×C₈, C₂×C₃²×C₄²×C₅², C₃×C₄²×C₅²×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.