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C₁₃×#10620323 #22555438

order	8541
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×#10620323

Splittings

Fitting, socle, Hall	C₁₃×C₇₃ ⋊ C₉
derived, Sylow	C₇₃ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	#10620323
commutator, hypocenter	C₇₃	C₉×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₇₃	C₉
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₃×#10620323⋊C₂, #10620323⋊D₁₃, D₁₃×#10620323, …
maximal normal subgroup of	C₁₃×#10620323⋊C₂, #10620323⋊D₁₃, D₁₃×#10620323, …
maximal quotient of	C₂×C₁₃×#10620323, C₁₃×C₂²⋊#10620323

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8541, 7);