Finite Group Databasebeta

← Prev (#42124532) Next (#42124534) →

C₂×D₃₁⋊(C₅²⋊C₉) #42124533

order	27900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×D₃₁⋊(C₅²⋊C₉)
unambiguous semidirect product	D₃₁⋊(C₂×C₅²⋊C₉)
unambiguous semidirect product	(C₂×D₃₁)⋊(C₅²⋊C₉)

Splittings

derived, Hall	C₅²×C₃₁ ⋊ C₂²×C₉
Hall	C₅²⋊(C₃₁⋊C₉) ⋊ C₂²
Hall	C₂×C₅²×D₃₁ ⋊ C₉
Hall	C₂×D₃₁ ⋊ C₅²⋊C₉
Sylow	C₃₁ ⋊ C₂²×C₅²⋊C₉
Sylow	C₅² ⋊ C₂×D₃₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃₁⋊(C₅²⋊C₃)
commutator, hypocenter	C₅²×C₃₁	C₂²×C₉
Frattini	C₃	C₂×D₃₁⋊(C₅²⋊C₃)
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₅²×D₃₁	C₃
cosocle	C₃×C₅²×C₃₁	C₂²×C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₂×C₃

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

882 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 280);