Finite Group Databasebeta

← Prev (#26043469) Next (#26043471) →

C₁₃×C₂²⋊(C₅²⋊C₉) #26043470

order	11700
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₁₃×C₂²⋊(C₅²⋊C₉)
unambiguous semidirect product	C₂²⋊(C₁₃×C₅²⋊C₉)
unambiguous semidirect product	C₅²⋊(C₁₃×C₂²⋊C₉)

Splittings

derived, Hall	C₂²×C₅² ⋊ C₉×C₁₃
Hall	C₂²×C₅²×C₁₃ ⋊ C₉
Hall	C₅²×C₁₃ ⋊ C₂²⋊C₉
Hall	C₂²×C₁₃ ⋊ C₅²⋊C₉
Sylow	C₅² ⋊ C₁₃×C₂²⋊C₉
Sylow	C₂² ⋊ C₁₃×C₅²⋊C₉

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 317);