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C₁₃×C₇₉⋊C₉ #22604454

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

Aliases

C₁₃×C₇₉⋊C₉

Splittings

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

Subgroups

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

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃×C₇₉⋊C₉, C₁₃×D₇₉⋊C₉, D₁₃×C₇₉⋊C₉, …
maximal normal subgroup of	C₂×C₁₃×C₇₉⋊C₉, C₁₃×D₇₉⋊C₉, D₁₃×C₇₉⋊C₉, …
maximal quotient of	C₂×C₁₃×C₇₉⋊C₉, C₁₃×C₂²⋊(C₇₉⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 5);