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C₉×D₃₁⋊C₂₅ #28358361

order	13950
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₃₁⋊C₂₅
unambiguous semidirect product	(C₉×D₃₁)⋊C₂₅

Splittings

derived, Sylow	C₃₁ ⋊ C₂×C₉×C₂₅
Hall	C₉×C₃₁⋊C₂₅ ⋊ C₂
Hall	C₃₁⋊C₂₅ ⋊ C₂×C₉
Hall	C₉×D₃₁ ⋊ C₂₅
Hall	C₉×C₃₁ ⋊ C₂×C₂₅
Hall	D₃₁ ⋊ C₉×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₃₁⋊C₅
commutator, hypocenter	C₃₁	C₂×C₉×C₂₅
Frattini	C₃×C₅	C₃×D₃₁⋊C₅
Fitting	C₅×C₉×C₃₁	C₂×C₅
socle, cosocle	C₃×C₅×C₃₁	C₂×C₃×C₅
prime radical	C₃×C₅×D₃₁	C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

585 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₃₁⋊C₂₅, C₂×C₉×D₃₁⋊C₂₅
maximal normal subgroup of	D₉×D₃₁⋊C₂₅, C₂×C₉×D₃₁⋊C₂₅
maximal quotient of	C₉×Dic₃₁⋊C₂₅, C₂×C₉×D₃₁⋊C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 4);