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D₃×C₇×C₁₃×D₇ #21439759

order	7644
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×C₁₃×D₇
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₇×C₁₃)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₇×C₁₃)
unambiguous semidirect product	D₂₁⋊(C₂×C₇×C₁₃)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₃ ⋊ C₂²
derived	C₃×C₇ ⋊ C₂²×C₇×C₁₃
Hall	C₇²×C₁₃ ⋊ C₂×D₃
Hall	C₃×C₇² ⋊ C₂²×C₁₃
Sylow	C₇² ⋊ C₂×D₃×C₁₃
Hall	C₃×C₁₃ ⋊ C₂×C₇×D₇
Sylow	C₃ ⋊ C₂×C₇×C₁₃×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇×C₁₃

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₁₃×D₇×D₉, D₃×C₁₃×#64418, D₃×C₇×C₁₃×AGL(1,𝔽₇), …
maximal normal subgroup of	D₃×C₇×C₁₃×AGL(1,𝔽₇), D₃×C₇×#10587721, D₃×C₇×#10587720, …
maximal quotient of	C₇×C₁₃×D₇×D₉, C₃×D₃×C₇×C₁₃×D₇, D₃×C₇×C₁₃×D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 328);