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C₉×D₆₅₅ #26044579

order	11790
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₆₅₅
unambiguous semidirect product	C₅⋊(C₉×D₁₃₁)
unambiguous semidirect product	C₁₃₁⋊(C₉×D₅)

Splittings

Fitting, Hall	C₅×C₉×C₁₃₁ ⋊ C₂
derived, Hall	C₅×C₁₃₁ ⋊ C₂×C₉
Hall	C₉×C₁₃₁ ⋊ D₅
Sylow	C₁₃₁ ⋊ C₉×D₅
Hall	C₅×C₉ ⋊ D₁₃₁
Sylow	C₅ ⋊ C₉×D₁₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₆₅₅
commutator, hypocenter	C₅×C₁₃₁	C₂×C₉
Frattini	C₃	C₃×D₆₅₅
Fitting	C₅×C₉×C₁₃₁	C₂
socle, cosocle	C₃×C₅×C₁₃₁	C₂×C₃
prime radical	C₃×D₆₅₅	C₃
LCS	G ▷ C₅×C₁₃₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2961 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₅×D₁₃₁, D₉×D₆₅₅, D₄₅⋊D₁₃₁, …
maximal normal subgroup of	C₉×D₅×D₁₃₁, D₉×D₆₅₅, D₄₅⋊D₁₃₁, …
maximal quotient of	C₉×Dic₆₅₅, C₂×C₉×D₆₅₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11790, 5);