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C₇×C₇₉⋊C₉ #19097320

order	4977
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

609 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×C₂²⋊(C₇₉⋊C₉), C₅×C₇×C₇₉⋊C₉, C₄₉×C₇₉⋊C₉, …
maximal normal subgroup of	C₅×C₇×C₇₉⋊C₉, C₄₉×C₇₉⋊C₉, C₇²×C₇₉⋊C₉
maximal quotient of	C₇×C₂²⋊(C₇₉⋊C₉), C₅×C₇×C₇₉⋊C₉, C₄₉×C₇₉⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4977, 3);