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C₃×C₇×D₇×C₁₃⋊C₃ #26039588

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₇ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₇×D₇×C₁₃⋊C₃

Splittings

Fitting, socle	C₃×C₇²×C₁₃ ⋊ C₂×C₃
derived	C₇×C₁₃ ⋊ C₂×C₃²×C₇
Hall	C₃×C₇²×C₁₃⋊C₃ ⋊ C₂
Hall	C₇×C₁₃×D₇ ⋊ C₃²
Hall	C₇²×C₁₃ ⋊ C₂×C₃²
Sylow	C₇² ⋊ C₂×C₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ C₃²×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₇

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₇×D₇×D₁₃⋊C₃, C₃×D₇×(C₁₃⋊C₃)⋊D₇, C₃×D₇²×C₁₃⋊C₃, …
maximal normal subgroup of	C₃×C₇×D₇×D₁₃⋊C₃, C₃×D₇×(C₁₃⋊C₃)⋊D₇, C₃×D₇²×C₁₃⋊C₃, …
maximal quotient of	C₃×C₇×Dic₇×C₁₃⋊C₃, C₂×C₃×C₇×D₇×C₁₃⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 231);