Finite Group Databasebeta

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D₉×C₂₅×C₃₁ #28358372

order	13950
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₂₅×C₃₁
unambiguous semidirect product	C₉⋊(C₂×C₂₅×C₃₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅×C₃₁	D₉
commutator, hypocenter	C₉	C₂×C₂₅×C₃₁
Frattini	C₃×C₅	C₅×D₃×C₃₁
Fitting	C₉×C₂₅×C₃₁	C₂
socle	C₃×C₅×C₃₁	C₅×D₃
prime radical	C₅×D₉×C₃₁	C₅
cosocle	C₅×C₉	C₂×C₅×C₃₁
LCS	G ▷ C₉
UCS	C₁ ◁ C₂₅×C₃₁

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4650 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₂₅×D₃₁, D₉×C₃₁×D₂₅, D₉×D₇₇₅, …
maximal normal subgroup of	D₉×C₂₅×D₃₁, D₉×C₃₁×D₂₅, D₉×D₇₇₅, …
maximal quotient of	C₂₅×C₃₁×Dic₉, C₂×D₉×C₂₅×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 15);