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C₃×C₂₂₃⋊C₉ #20258258

order	6021
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₂₂₃⋊C₉
unambiguous semidirect product	(C₃×C₂₂₃)⋊C₉

Splittings

C₂₂₃ ⋊ C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	C₂₂₃⋊C₃
commutator, hypocenter	C₂₂₃	C₃×C₉
Frattini	C₃	C₃×C₂₂₃⋊C₃
Fitting, socle	C₃²×C₂₂₃	C₃
LCS	G ▷ C₂₂₃
UCS	C₁ ◁ C₃²

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

693 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×C₂₂₃⋊C₉, (C₃×C₂₂₃⋊C₃)⋊C₉, C₃²⋊(C₂₂₃⋊C₉), …
maximal normal subgroup of	C₉×C₂₂₃⋊C₉, (C₃×C₂₂₃⋊C₃)⋊C₉, C₃²⋊(C₂₂₃⋊C₉), …
maximal quotient of	C₉×C₂₂₃⋊C₉, C₃²⋊(C₂₂₃⋊C₉), #31825580, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6021, 8);