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C₇₉×D₇⋊C₉ #23755776

order	9954
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₉×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₉×C₇₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₇₉)

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₇₉
Hall	C₇⋊C₉×C₇₉ ⋊ C₂
Hall	D₇×C₇₉ ⋊ C₉
Hall	C₇×C₇₉ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₇₉
Hall	D₇ ⋊ C₉×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₇₉
Frattini	C₃	AGL(1,𝔽₇)×C₇₉
Fitting, socle	C₃×C₇×C₇₉	C₂×C₃
prime radical	C₃×D₇×C₇₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₇₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₇₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇⋊C₉×D₇₉, C₂×C₇₉×D₇⋊C₉
maximal normal subgroup of	D₇⋊C₉×D₇₉, C₂×C₇₉×D₇⋊C₉
maximal quotient of	C₇₉×Dic₇⋊C₉, C₂×C₇₉×D₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9954, 18);