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C₁₃×C₂₅×C₃₁ #23758586

order	10075
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃²×C₄²×C₅² (order 7200) · Inn(G) = C₁ · Out(G) = C₂×C₃²×C₄²×C₅²
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₀₇₅
abelian	C₁₃×C₂₅×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₁₃×C₃₁
socle, prime radical	C₅×C₁₃×C₃₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10075 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₁₃×C₂₅×C₃₁⋊C₃, C₂₅×C₃₁×C₁₃⋊C₃, C₂₅×#11925882, …
maximal subgroup of	C₂×C₁₃×C₂₅×C₃₁, C₁₃×C₂₅×D₃₁, C₂₅×D₁₃×C₃₁, …
maximal normal subgroup of	C₂×C₁₃×C₂₅×C₃₁, C₁₃×C₂₅×D₃₁, C₂₅×D₁₃×C₃₁, …
maximal quotient of	C₂×C₁₃×C₂₅×C₃₁, C₃×C₁₃×C₂₅×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10075, 1);