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C₉×C₇⋊D₉₁ #26039499

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

Aliases

C₉×C₇⋊D₉₁

Splittings

Fitting, Hall	C₇²×C₉×C₁₃ ⋊ C₂
derived, Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₇²×C₉ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ C₇⋊D₇
Sylow	C₇² ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₇⋊D₉₁
commutator, hypocenter	C₇²×C₁₃	C₂×C₉
Frattini	C₃	C₃×C₇⋊D₉₁
Fitting	C₇²×C₉×C₁₃	C₂
socle, cosocle	C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₃×C₇⋊D₉₁	C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₉

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×C₇⋊D₇, C₉×D₇×D₉₁, C₉×#14579330, …
maximal normal subgroup of	C₉×D₁₃×C₇⋊D₇, C₉×D₇×D₉₁, C₉×#14579330, …
maximal quotient of	C₉×C₇⋊Dic₉₁, C₂×C₉×C₇⋊D₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 142);