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C₇⋊C₉×D₉₁ #26039481

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇⋊C₉×D₉₁

Splittings

derived, Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₇×C₁₃×C₇⋊C₉ ⋊ C₂
Hall	C₇×D₉₁ ⋊ C₉
Hall	C₇×C₇⋊C₉ ⋊ D₁₃
Sylow	C₇² ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ D₇×C₇⋊C₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₉₁
commutator, hypocenter	C₇²×C₁₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₃×C₇×D₉₁	C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

705 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇⋊C₉×D₉₁, ((C₇⋊C₉)⋊D₇)⋊D₁₃, D₇×D₁₃×C₇⋊C₉, …
maximal normal subgroup of	D₇⋊C₉×D₉₁, ((C₇⋊C₉)⋊D₇)⋊D₁₃, D₇×D₁₃×C₇⋊C₉, …
maximal quotient of	C₇⋊C₉×Dic₉₁, C₂×C₇⋊C₉×D₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 124);