Finite Group Databasebeta

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C₃²×C₇×D₉₁ #26039719

order	11466
isoclinism	isoclinic class of D₉₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₇ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₇×D₉₁

Splittings

Fitting, socle, Hall	C₃²×C₇²×C₁₃ ⋊ C₂
derived	C₇×C₁₃ ⋊ C₂×C₃²×C₇
Hall	C₇²×C₁₃ ⋊ C₂×C₃²
Hall	C₃²×C₇² ⋊ D₁₃
Hall	C₃²×C₁₃ ⋊ C₇×D₇
Sylow	C₇² ⋊ C₃²×D₁₃
Sylow	C₁₃ ⋊ C₃²×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₉₁
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃²×C₇

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2961 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₇×D₇×D₁₃, C₃²×D₇×D₉₁, C₃²×(C₇⋊D₇)⋊D₁₃, …
maximal normal subgroup of	C₃²×C₇×D₇×D₁₃, C₃²×D₇×D₉₁, C₃²×(C₇⋊D₇)⋊D₁₃, …
maximal quotient of	C₃²×C₇×Dic₉₁, C₂×C₃²×C₇×D₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 362);