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D₇⋊C₉×C₁₃₁ #30658208

order	16506
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₃₁
unambiguous semidirect product	D₇⋊(C₉×C₁₃₁)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₃₁)
unambiguous semidirect product	(D₇×C₁₃₁)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₃₁
Hall	C₇⋊C₉×C₁₃₁ ⋊ C₂
Hall	D₇×C₁₃₁ ⋊ C₉
Hall	C₇×C₁₃₁ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₃₁
Hall	D₇ ⋊ C₉×C₁₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃₁	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₃₁
Frattini	C₃	AGL(1,𝔽₇)×C₁₃₁
Fitting, socle	C₃×C₇×C₁₃₁	C₂×C₃
prime radical	C₃×D₇×C₁₃₁	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8253

Conjugacy classes & character table

2751 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇⋊C₉×D₁₃₁, C₂×D₇⋊C₉×C₁₃₁
maximal normal subgroup of	D₇⋊C₉×D₁₃₁, C₂×D₇⋊C₉×C₁₃₁
maximal quotient of	C₁₃₁×Dic₇⋊C₉, C₂×D₇⋊C₉×C₁₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16506, 11);