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C₂₃×C₃₁⋊C₉ #20264382

order	6417
isoclinism	isoclinic class of C₃₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×C₃₁⋊C₉
unambiguous semidirect product	C₃₁⋊(C₉×C₂₃)
unambiguous semidirect product	(C₂₃×C₃₁)⋊C₉

Splittings

derived, Sylow	C₃₁ ⋊ C₉×C₂₃
Hall	C₂₃×C₃₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₃	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₉×C₂₃
Frattini	C₃	C₂₃×C₃₁⋊C₃
Fitting, socle	C₃×C₂₃×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₂₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

897 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×C₃₁⋊C₉, C₂₃×D₃₁⋊C₉, D₂₃×C₃₁⋊C₉, …
maximal normal subgroup of	C₂×C₂₃×C₃₁⋊C₉, C₂₃×D₃₁⋊C₉, D₂₃×C₃₁⋊C₉, …
maximal quotient of	C₂×C₂₃×C₃₁⋊C₉, C₂₃×C₂²⋊(C₃₁⋊C₉), C₅×C₂₃×C₃₁⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6417, 2);