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C₂×C₇×C₁₃×C₇⋊C₉ #26039487

order	11466
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇×C₁₃×C₇⋊C₉
unambiguous semidirect product	(C₂×C₇)⋊(C₇×C₉×C₁₃)

Splittings

derived	C₇ ⋊ C₂×C₇×C₉×C₁₃
Hall	C₂×C₇²×C₁₃ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₂×C₇² ⋊ C₉×C₁₃
Sylow	C₇² ⋊ C₂×C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₃	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₇×C₉×C₁₃
Frattini	C₃	C₂×C₇×C₁₃×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₃	C₃
cosocle	C₃×C₇	C₂×C₃×C₇×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₇×C₁₃

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₁₃×Dic₇⋊C₉, C₇×(C₇⋊C₉)⋊Dic₁₃, C₇×Dic₁₃×C₇⋊C₉, …
maximal normal subgroup of	C₇×C₁₃×Dic₇⋊C₉, C₇×(C₇⋊C₉)⋊Dic₁₃, C₇×Dic₁₃×C₇⋊C₉, …
maximal quotient of	C₄×C₇×C₁₃×C₇⋊C₉, C₂²×C₇×C₁₃×C₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 130);