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C₂×C₉×C₂₅×C₃₁ #28358358

order	13950
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₉₅₀
abelian	C₂×C₉×C₂₅×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅	C₂×C₃×C₅×C₃₁
socle, prime radical	C₂×C₃×C₅×C₃₁	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13950 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₉₅₀, D₂₇₉₀₀
maximal subgroup of	C₄×C₉×C₂₅×C₃₁, C₉×C₂₅×Dic₃₁, C₉×C₃₁×Dic₂₅, …
maximal normal subgroup of	C₄×C₉×C₂₅×C₃₁, C₉×C₂₅×Dic₃₁, C₉×C₃₁×Dic₂₅, …
maximal quotient of	C₄×C₉×C₂₅×C₃₁, C₂²×C₉×C₂₅×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 1);