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C₃×C₄³×C₂₅ #72184236

order	4800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3440640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

abelian	C₃×C₄³×C₂₅
multiplicative	(ℤ/6565)ˣ, (ℤ/13130)ˣ

Subgroups

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

774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₈×C₂₅, C₂×C₃×C₄³×C₂₅, C₄³×C₉×C₂₅, …
maximal normal subgroup of	C₃×C₄²×C₈×C₂₅, C₂×C₃×C₄³×C₂₅, C₄³×C₉×C₂₅, …
maximal quotient of	C₃×C₄²×C₈×C₂₅, C₂×C₃×C₄³×C₂₅, C₄³×C₉×C₂₅, …
automorphism group of	C₅×C₁₃×C₁₀₁
outer automorphism group of	C₅×C₁₃×C₁₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.