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C₇⋊C₉×D₆₁ #21440249

order	7686
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇⋊C₉×D₆₁

Splittings

derived, Hall	C₇×C₆₁ ⋊ C₂×C₉
Hall	C₆₁×C₇⋊C₉ ⋊ C₂
Hall	C₇×D₆₁ ⋊ C₉
Sylow	C₆₁ ⋊ C₂×C₇⋊C₉
Sylow	C₇ ⋊ C₉×D₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₆₁
commutator, hypocenter	C₇×C₆₁	C₂×C₉
Fitting, socle	C₃×C₇×C₆₁	C₂×C₃
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₇⋊C₉)⋊#6923, D₆₁×D₇⋊C₉, C₇⋊C₉×#6923, …
maximal normal subgroup of	(C₇⋊C₉)⋊#6923, D₆₁×D₇⋊C₉, C₇⋊C₉×#6923, …
maximal quotient of	C₇⋊C₉×Dic₆₁, C₂×C₇⋊C₉×D₆₁, C₅×C₇⋊C₉×D₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7686, 14);