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D₇⋊C₉×C₁₃₉ #31776105

order	17514
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₃₉
unambiguous semidirect product	D₇⋊(C₉×C₁₃₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₃₉)

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₃₉
Hall	C₇⋊C₉×C₁₃₉ ⋊ C₂
Hall	D₇×C₁₃₉ ⋊ C₉
Hall	C₇×C₁₃₉ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₃₉
Hall	D₇ ⋊ C₉×C₁₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₃₉
Frattini	C₃	AGL(1,𝔽₇)×C₁₃₉
Fitting, socle	C₃×C₇×C₁₃₉	C₂×C₃
prime radical	C₃×D₇×C₁₃₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8757

Conjugacy classes & character table

2919 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇⋊C₉×D₁₃₉, C₂×D₇⋊C₉×C₁₃₉
maximal normal subgroup of	D₇⋊C₉×D₁₃₉, C₂×D₇⋊C₉×C₁₃₉
maximal quotient of	C₁₃₉×Dic₇⋊C₉, C₂×D₇⋊C₉×C₁₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17514, 18);