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C₇×D₇₉⋊C₉ #23755771

order	9954
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₇₉⋊C₉
unambiguous semidirect product	D₇₉⋊(C₇×C₉)
unambiguous semidirect product	(C₇₉⋊C₉)⋊(C₂×C₇)

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

399 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9954, 13);