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C₂³×C₈×C₉×C₂₅ #72192562

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5160960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₈×C₉×C₂₅
multiplicative	(ℤ/43224)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₅	C₂⁴×C₃×C₅
socle, prime radical	C₂⁴×C₃×C₅	C₃×C₄×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

1521 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₉×C₁₆×C₂₅, C₂²×C₄×C₈×C₉×C₂₅, C₂⁴×C₈×C₉×C₂₅
maximal normal subgroup of	C₂³×C₉×C₁₆×C₂₅, C₂²×C₄×C₈×C₉×C₂₅, C₂⁴×C₈×C₉×C₂₅
maximal quotient of	C₂³×C₉×C₁₆×C₂₅, C₂²×C₄×C₈×C₉×C₂₅, C₂⁴×C₈×C₉×C₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.