Finite Group Databasebeta

← Prev (#28358372) Next (#28358374) →

C₂₅×D₂₇₉ #28358373

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

Aliases

direct product	C₂₅×D₂₇₉
unambiguous semidirect product	C₉⋊(C₂₅×D₃₁)

Splittings

Fitting, Hall	C₉×C₂₅×C₃₁ ⋊ C₂
derived, Hall	C₉×C₃₁ ⋊ C₂×C₂₅
Hall	C₂₅×C₃₁ ⋊ D₉
Hall	C₉×C₂₅ ⋊ D₃₁
Sylow	C₃₁ ⋊ D₉×C₂₅
Sylow	C₉ ⋊ C₂₅×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₂₇₉
commutator, hypocenter	C₉×C₃₁	C₂×C₂₅
Frattini	C₃×C₅	C₅×D₉₃
Fitting	C₉×C₂₅×C₃₁	C₂
socle	C₃×C₅×C₃₁	C₅×D₃
prime radical	C₅×D₂₇₉	C₅
cosocle	C₅×C₉×C₃₁	C₂×C₅
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3525 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×C₂₅×D₃₁, D₂₅×D₂₇₉, D₂₂₅⋊D₃₁, …
maximal normal subgroup of	D₉×C₂₅×D₃₁, D₂₅×D₂₇₉, D₂₂₅⋊D₃₁, …
maximal quotient of	C₂₅×Dic₂₇₉, C₂×C₂₅×D₂₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 16);