Finite Group Databasebeta

← Prev (#23755771) Next (#23755773) →

C₇⋊C₉×D₇₉ #23755772

order	9954
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇⋊C₉×D₇₉

Splittings

derived, Hall	C₇×C₇₉ ⋊ C₂×C₉
Hall	C₇⋊C₉×C₇₉ ⋊ C₂
Hall	C₇×D₇₉ ⋊ C₉
Sylow	C₇₉ ⋊ C₂×C₇⋊C₉
Sylow	C₇ ⋊ C₉×D₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	ΓL(1,𝔽₈)×D₇₉
commutator, hypocenter	C₇×C₇₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₇×C₇₉	C₂×C₃
prime radical	C₃×C₇×D₇₉	C₃
LCS	G ▷ C₇×C₇₉
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

615 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇⋊C₉×D₇₉, C₂×C₇⋊C₉×D₇₉
maximal normal subgroup of	D₇⋊C₉×D₇₉, C₂×C₇⋊C₉×D₇₉
maximal quotient of	C₇⋊C₉×Dic₇₉, C₂×C₇⋊C₉×D₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9954, 14);