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C₂³×C₄²×C₂₅ #72182946

order	3200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1321205760
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian	C₂³×C₄²×C₂₅
multiplicative	(ℤ/12120)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₅	C₂⁵×C₅
socle, prime radical	C₂⁵×C₅	C₂²×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

4500 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₈×C₂₅, C₂²×C₄³×C₂₅, C₂⁴×C₄²×C₂₅, …
maximal normal subgroup of	C₂³×C₄×C₈×C₂₅, C₂²×C₄³×C₂₅, C₂⁴×C₄²×C₂₅, …
maximal quotient of	C₂³×C₄×C₈×C₂₅, C₂²×C₄³×C₂₅, C₂⁴×C₄²×C₂₅, …
automorphism group of	C₃×C₅×C₈×C₁₀₁
outer automorphism group of	C₃×C₅×C₈×C₁₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.