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C₃×C₄²×C₅×C₃₂ #72186596

order	7680
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3145728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

C₃×C₄²×C₅×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₆	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

1416 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₅×C₆₄, C₃×C₄×C₅×C₈×C₃₂, C₂×C₃×C₄²×C₅×C₃₂, …
maximal normal subgroup of	C₃×C₄²×C₅×C₆₄, C₃×C₄×C₅×C₈×C₃₂, C₂×C₃×C₄²×C₅×C₃₂, …
maximal quotient of	C₃×C₄²×C₅×C₆₄, C₃×C₄×C₅×C₈×C₃₂, C₂×C₃×C₄²×C₅×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.