Finite Group Databasebeta

← Prev (#26043403) Next (#26043405) →

C₂×D₁₃⋊(C₅²⋊C₉) #26043404

order	11700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×D₁₃⋊(C₅²⋊C₉)
unambiguous semidirect product	D₁₃⋊(C₂×C₅²⋊C₉)
unambiguous semidirect product	(C₂×D₁₃)⋊(C₅²⋊C₉)

Splittings

derived, Hall	C₅²×C₁₃ ⋊ C₂²×C₉
Hall	C₁₃⋊(C₅²⋊C₉) ⋊ C₂²
Hall	C₂×C₅²×D₁₃ ⋊ C₉
Hall	C₂×D₁₃ ⋊ C₅²⋊C₉
Sylow	C₅² ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂²×C₅²⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₃⋊(C₅²⋊C₃)
commutator, hypocenter	C₅²×C₁₃	C₂²×C₉
Frattini	C₃	C₂×D₁₃⋊(C₅²⋊C₃)
Fitting, socle	C₂×C₃×C₅²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₅²×D₁₃	C₃
cosocle	C₃×C₅²×C₁₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₂×C₃

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

432 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 251);