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C₇₉×Dic₇⋊C₉ #34092557

order	19908
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇₉×Dic₇⋊C₉
unambiguous semidirect product	Dic₇⋊(C₉×C₇₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₄×C₇₉)

Splittings

derived, Sylow	C₇ ⋊ C₄×C₉×C₇₉
Hall	C₇⋊C₉×C₇₉ ⋊ C₄
Hall	Dic₇×C₇₉ ⋊ C₉
Hall	C₇×C₇₉ ⋊ C₄×C₉
Hall	C₇⋊C₉ ⋊ C₄×C₇₉
Hall	Dic₇ ⋊ C₉×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₄×C₉×C₇₉
Frattini	C₂×C₃	AGL(1,𝔽₇)×C₇₉
Fitting, socle, prime radical	C₂×C₃×C₇×C₇₉	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₇₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₇₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 19908

Conjugacy classes & character table

3318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19908, 18);