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C₇⋊C₉×C₁₃₉ #22576802

order	8757
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₃₉
Frattini	C₃	ΓL(1,𝔽₈)×C₁₃₉
Fitting, socle	C₃×C₇×C₁₃₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2085 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇⋊C₉×C₁₃₉, C₇⋊C₉×D₁₃₉, D₇⋊C₉×C₁₃₉, …
maximal normal subgroup of	C₂×C₇⋊C₉×C₁₃₉, C₇⋊C₉×D₁₃₉, D₇⋊C₉×C₁₃₉, …
maximal quotient of	C₂×C₇⋊C₉×C₁₃₉, C₁₃₉×C₂²⋊(C₇⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8757, 2);