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C₇×C₁₃⋊C₃×D₂₁ #26039647

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₃⋊C₃×D₂₁
unambiguous semidirect product	C₃⋊(C₇×D₇×C₁₃⋊C₃)

Splittings

Fitting, socle	C₃×C₇²×C₁₃ ⋊ C₂×C₃
derived	C₃×C₇×C₁₃ ⋊ C₂×C₃×C₇
Hall	C₃×C₇²×C₁₃⋊C₃ ⋊ C₂
Hall	C₇²×C₁₃ ⋊ C₃×D₃
Hall	C₃×C₁₃⋊C₃ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ C₃×C₇×D₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇	C₁₃⋊C₃×D₂₁
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₇

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

588 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×D₂₁×D₁₃⋊C₃, C₇×(C₃⋊(D₁₃⋊C₃))⋊D₇, D₃×C₇×D₇×C₁₃⋊C₃, …
maximal normal subgroup of	C₇×D₂₁×D₁₃⋊C₃, C₇×(C₃⋊(D₁₃⋊C₃))⋊D₇, D₃×C₇×D₇×C₁₃⋊C₃, …
maximal quotient of	C₇×C₁₃⋊C₃×Dic₂₁, C₂×C₇×C₁₃⋊C₃×D₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 290);