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C₉×C₇₉⋊C₁₃ #22604452

order	9243
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₇₉⋊C₁₃
unambiguous semidirect product	(C₉×C₇₉)⋊C₁₃

Splittings

Fitting, Hall	C₉×C₇₉ ⋊ C₁₃
derived, Sylow	C₇₉ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₇₉⋊C₁₃
commutator, hypocenter	C₇₉	C₉×C₁₃
Frattini	C₃	C₃×C₇₉⋊C₁₃
Fitting	C₉×C₇₉	C₁₃
socle	C₃×C₇₉	C₃×C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₉×C₇₉⋊C₁₃, C₉×D₇₉⋊C₁₃, D₉×C₇₉⋊C₁₃, …
maximal normal subgroup of	C₂×C₉×C₇₉⋊C₁₃, C₉×D₇₉⋊C₁₃, D₉×C₇₉⋊C₁₃, …
maximal quotient of	C₂×C₉×C₇₉⋊C₁₃, C₂²⋊C₉×C₇₉⋊C₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 3);