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C₉×C₅⋊D₁₁₅ #23780358

order	10350
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₉×C₅⋊D₁₁₅
unambiguous semidirect product	C₅⋊(C₉×D₁₁₅)
unambiguous semidirect product	C₂₃⋊(C₉×C₅⋊D₅)

Splittings

Fitting, Hall	C₅²×C₉×C₂₃ ⋊ C₂
derived, Hall	C₅²×C₂₃ ⋊ C₂×C₉
Hall	C₅²×C₉ ⋊ D₂₃
Hall	C₉×C₂₃ ⋊ C₅⋊D₅
Sylow	C₅² ⋊ C₉×D₂₃
Sylow	C₂₃ ⋊ C₉×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₅⋊D₁₁₅
commutator, hypocenter	C₅²×C₂₃	C₂×C₉
Frattini	C₃	C₃×C₅⋊D₁₁₅
Fitting	C₅²×C₉×C₂₃	C₂
socle, cosocle	C₃×C₅²×C₂₃	C₂×C₃
prime radical	C₃×C₅⋊D₁₁₅	C₃
LCS	G ▷ C₅²×C₂₃
UCS	C₁ ◁ C₉

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2601 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₃×C₅⋊D₅, C₉×D₅×D₁₁₅, D₉×C₅⋊D₁₁₅, …
maximal normal subgroup of	C₉×D₂₃×C₅⋊D₅, C₉×D₅×D₁₁₅, D₉×C₅⋊D₁₁₅, …
maximal quotient of	C₉×C₂₃⋊#1039, C₂×C₉×C₅⋊D₁₁₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 32);