Finite Group Databasebeta

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C₃×C₁₁×C₁₃×C₂₅ #24924327

order	10725
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₅² (order 4800) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₅²
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₇₂₅
abelian	C₃×C₁₁×C₁₃×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃×C₅×C₁₁×C₁₃
socle, prime radical	C₃×C₅×C₁₁×C₁₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10725 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₇₂₅
Fitting subgroup of	C₃×C₁₁×C₂₅×D₁₃, C₃×C₁₃×D₁₁×C₂₅, C₃×C₂₅×D₁₄₃, …
maximal subgroup of	C₂×C₃×C₁₁×C₁₃×C₂₅, C₃×C₁₁×C₂₅×D₁₃, C₃×C₁₃×D₁₁×C₂₅, …
maximal normal subgroup of	C₂×C₃×C₁₁×C₁₃×C₂₅, C₃×C₁₁×C₂₅×D₁₃, C₃×C₁₃×D₁₁×C₂₅, …
maximal quotient of	C₂×C₃×C₁₁×C₁₃×C₂₅, C₉×C₁₁×C₁₃×C₂₅, C₃²×C₁₁×C₁₃×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 1);