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C₁₃×D₇×C₇⋊C₉ #26039476

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×D₇×C₇⋊C₉

Splittings

derived, Sylow	C₇² ⋊ C₂×C₉×C₁₃
Hall	C₇×C₁₃×C₇⋊C₉ ⋊ C₂
Hall	C₇×C₁₃×D₇ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₂×C₁₃
Hall	C₇×D₇ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂×C₉×C₁₃
Frattini	C₃	C₁₃×D₇×ΓL(1,𝔽₈)
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₃×C₇×C₁₃×D₇	C₃
cosocle	C₃×C₇²	C₂×C₃×C₁₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₃

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₃×D₇×D₇⋊C₉, D₇×(C₇⋊C₉)⋊D₁₃, D₇×D₁₃×C₇⋊C₉, …
maximal normal subgroup of	C₁₃×D₇×D₇⋊C₉, D₇×(C₇⋊C₉)⋊D₁₃, D₇×D₁₃×C₇⋊C₉, …
maximal quotient of	C₁₃×Dic₇×C₇⋊C₉, C₂×C₁₃×D₇×C₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 119);