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C₇₉×C₂²⋊(C₇⋊C₉) #34092594

order	19908
automorphism	?
homology	Abelianization (H₁) = C₉×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇₉×C₂²⋊(C₇⋊C₉)
unambiguous semidirect product	C₂²⋊(C₇⋊C₉×C₇₉)
unambiguous semidirect product	C₇⋊(C₂²⋊C₉×C₇₉)

Splittings

derived, Hall	C₂²×C₇ ⋊ C₉×C₇₉
Hall	C₂²×C₇×C₇₉ ⋊ C₉
Hall	C₇×C₇₉ ⋊ C₂²⋊C₉
Hall	C₂²×C₇₉ ⋊ C₇⋊C₉
Sylow	C₇ ⋊ C₂²⋊C₉×C₇₉
Sylow	C₂² ⋊ C₇⋊C₉×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₉	C₂²⋊ΓL(1,𝔽₈)
commutator, hypocenter	C₂²×C₇	C₉×C₇₉
Frattini	C₃	C₇₉×C₂²⋊ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂²×C₃×C₇×C₇₉	C₃
cosocle	C₂²×C₃×C₇	C₃×C₇₉
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₃×C₇₉

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9954

Conjugacy classes & character table

2844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19908, 55);