Finite Group Databasebeta

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C₉×(C₅⋊D₅)⋊D₁₃ #26043428

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

Aliases

C₉×(C₅⋊D₅)⋊D₁₃

Splittings

Fitting, Hall	C₅²×C₉×C₁₃ ⋊ C₂²
derived, Hall	C₅²×C₁₃ ⋊ C₂²×C₉
Hall	C₅²×C₉ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ D₅²
Sylow	C₅² ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₉	(C₅⋊D₅)⋊D₁₃
commutator, hypocenter	C₅²×C₁₃	C₂²×C₉
Frattini	C₃	C₃×(C₅⋊D₅)⋊D₁₃
Fitting	C₅²×C₉×C₁₃	C₂²
socle, cosocle	C₃×C₅²×C₁₃	C₂²×C₃
prime radical	C₃×(C₅⋊D₅)⋊D₁₃	C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₉

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

900 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 275);