Finite Group Databasebeta

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C₇₃×D₆₃ #22604086

order	9198
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₃×D₆₃
unambiguous semidirect product	C₇⋊(D₉×C₇₃)
unambiguous semidirect product	C₉⋊(D₇×C₇₃)

Splittings

Fitting, Hall	C₇×C₉×C₇₃ ⋊ C₂
derived, Hall	C₇×C₉ ⋊ C₂×C₇₃
Hall	C₉×C₇₃ ⋊ D₇
Hall	C₇×C₇₃ ⋊ D₉
Sylow	C₉ ⋊ D₇×C₇₃
Sylow	C₇ ⋊ D₉×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₇₃	D₆₃
commutator, hypocenter	C₇×C₉	C₂×C₇₃
Frattini	C₃	D₂₁×C₇₃
Fitting	C₇×C₉×C₇₃	C₂
socle	C₃×C₇×C₇₃	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₇₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2409 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₆₃×D₇₃, D₇×D₉×C₇₃, D₆₃⋊D₇₃, …
maximal normal subgroup of	D₆₃×D₇₃, D₇×D₉×C₇₃, D₆₃⋊D₇₃, …
maximal quotient of	C₇₃×Dic₆₃, C₂×C₇₃×D₆₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9198, 11);