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C₇×D₁₃×C₇⋊C₉ #26039440

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇×D₁₃×C₇⋊C₉

Splittings

derived	C₇×C₁₃ ⋊ C₂×C₇×C₉
Hall	C₇×C₁₃×C₇⋊C₉ ⋊ C₂
Hall	C₇²×D₁₃ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₂×C₉
Sylow	C₇² ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₇×C₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	ΓL(1,𝔽₈)×D₁₃
commutator, hypocenter	C₇×C₁₃	C₂×C₇×C₉
Frattini	C₃	C₇×ΓL(1,𝔽₈)×D₁₃
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₃×C₇²×D₁₃	C₃
cosocle	C₃×C₇×C₁₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₇

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

840 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×(C₇⋊C₉)⋊#261, C₇×D₁₃×D₇⋊C₉, C₇×#261×C₇⋊C₉, …
maximal normal subgroup of	C₇×(C₇⋊C₉)⋊#261, C₇×D₁₃×D₇⋊C₉, C₇×#261×C₇⋊C₉, …
maximal quotient of	C₇×Dic₁₃×C₇⋊C₉, C₂×C₇×D₁₃×C₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 83);