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D₂₅×C₃₁⋊C₉ #28358365

order	13950
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₂₅×C₃₁⋊C₉
unambiguous semidirect product	C₂₅⋊(C₂×C₃₁⋊C₉)
unambiguous semidirect product	(C₃₁×D₂₅)⋊C₉

Splittings

derived, Hall	C₂₅×C₃₁ ⋊ C₂×C₉
Hall	C₂₅×C₃₁⋊C₉ ⋊ C₂
Hall	C₃₁×D₂₅ ⋊ C₉
Sylow	C₃₁ ⋊ C₉×D₂₅
Sylow	C₂₅ ⋊ C₂×C₃₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₂₅×C₃₁⋊C₃
commutator, hypocenter	C₂₅×C₃₁	C₂×C₉
Frattini	C₃×C₅	D₅×C₃₁⋊C₃
Fitting, cosocle	C₃×C₂₅×C₃₁	C₂×C₃
socle	C₃×C₅×C₃₁	C₃×D₅
prime radical	C₃×C₃₁×D₂₅	C₃
LCS	G ▷ C₂₅×C₃₁
UCS	C₁ ◁ C₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#1035×C₃₁⋊C₉, (C₃₁⋊C₉)⋊#1035, D₂₅×D₃₁⋊C₉, …
maximal normal subgroup of	#1035×C₃₁⋊C₉, (C₃₁⋊C₉)⋊#1035, D₂₅×D₃₁⋊C₉, …
maximal quotient of	Dic₂₅×C₃₁⋊C₉, C₂×D₂₅×C₃₁⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 8);