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C₃²×C₇₉⋊C₁₃ #22604459

order	9243
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₇₉⋊C₁₃
unambiguous semidirect product	(C₃²×C₇₉)⋊C₁₃

Splittings

Fitting, socle, Hall	C₃²×C₇₉ ⋊ C₁₃
derived, Sylow	C₇₉ ⋊ C₃²×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	C₇₉⋊C₁₃
commutator, hypocenter	C₇₉	C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇₉	C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃²

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃²×D₇₉⋊C₁₃, C₃×C₃⋊(D₇₉⋊C₁₃), C₃×D₃×C₇₉⋊C₁₃, …
maximal normal subgroup of	C₃²×D₇₉⋊C₁₃, C₃×C₃⋊(D₇₉⋊C₁₃), C₃×D₃×C₇₉⋊C₁₃, …
maximal quotient of	C₂×C₃²×C₇₉⋊C₁₃, C₃×A₄×C₇₉⋊C₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 10);