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C₁₃×D₇×D₂₁ #21439769

order	7644
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×D₇×D₂₁
unambiguous semidirect product	(C₃×D₇)⋊(C₁₃×D₇)
unambiguous semidirect product	(C₇×D₇)⋊(D₃×C₁₃)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₃ ⋊ C₂²
derived, Hall	C₃×C₇² ⋊ C₂²×C₁₃
Hall	C₇²×C₁₃ ⋊ C₂×D₃
Sylow	C₇² ⋊ C₂×D₃×C₁₃
Hall	C₃×C₁₃ ⋊ D₇²
Sylow	C₃ ⋊ C₁₃×D₇²

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₇×D₂₁
commutator, hypocenter	C₃×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₃

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₃×D₇×D₆₃, C₁₃×#64418⋊D₃, C₁₃×D₇×C₃⋊AGL(1,𝔽₇), …
maximal normal subgroup of	C₁₃×D₇×C₃⋊AGL(1,𝔽₇), D₇×C₃⋊#10587721, D₇×C₃⋊#10587720, …
maximal quotient of	C₁₃×D₇×D₆₃, C₃×C₁₃×D₇×D₂₁, C₁₃×D₂₁², …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 338);