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C₇⋊C₉×D₇₃ #22604089

order	9198
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇⋊C₉×D₇₃

Splittings

derived, Hall	C₇×C₇₃ ⋊ C₂×C₉
Hall	C₇⋊C₉×C₇₃ ⋊ C₂
Hall	C₇×D₇₃ ⋊ C₉
Sylow	C₇₃ ⋊ C₂×C₇⋊C₉
Sylow	C₇ ⋊ C₉×D₇₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₇₃
commutator, hypocenter	C₇×C₇₃	C₂×C₉
Fitting, socle	C₃×C₇×C₇₃	C₂×C₃
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₇⋊C₉)⋊#64408, D₇⋊C₉×D₇₃, C₇⋊C₉×#64408, …
maximal normal subgroup of	(C₇⋊C₉)⋊#64408, D₇⋊C₉×D₇₃, C₇⋊C₉×#64408, …
maximal quotient of	C₇⋊C₉×Dic₇₃, C₂×C₇⋊C₉×D₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9198, 14);