Finite Group Databasebeta

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C₃×C₄²×C₈×C₂₅ #72188314

order	9600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3932160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

C₃×C₄²×C₈×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄×C₅	C₂³×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

1224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₁₆×C₂₅, C₃×C₄×C₈²×C₂₅, C₂×C₃×C₄²×C₈×C₂₅, …
maximal normal subgroup of	C₃×C₄²×C₁₆×C₂₅, C₃×C₄×C₈²×C₂₅, C₂×C₃×C₄²×C₈×C₂₅, …
maximal quotient of	C₃×C₄²×C₁₆×C₂₅, C₃×C₄×C₈²×C₂₅, C₂×C₃×C₄²×C₈×C₂₅, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.