Finite Group Databasebeta

← Prev (#21439766) Next (#21439768) →

D₃×C₇⋊D₉₁ #21439767

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

Aliases

direct product	D₃×C₇⋊D₉₁
unambiguous semidirect product	(D₃×C₇)⋊D₉₁
unambiguous semidirect product	(D₃×C₁₃)⋊(C₇⋊D₇)

Splittings

Fitting, socle, derived, Hall	C₃×C₇²×C₁₃ ⋊ C₂²
Hall	C₇²×C₁₃ ⋊ C₂×D₃
Hall	C₃×C₇² ⋊ C₂×D₁₃
Sylow	C₇² ⋊ D₃×D₁₃
Hall	C₃×C₁₃ ⋊ C₂×C₇⋊D₇
Sylow	C₁₃ ⋊ D₃×C₇⋊D₇
Sylow	C₃ ⋊ C₂×C₇⋊D₉₁

Subgroups

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

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

960 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×C₇⋊D₉₁, D₃×#16838468, D₃×#16838469, …
maximal normal subgroup of	D₃×#16838468, D₃×#16838469, D₃×ΓL(1,𝔽₈)⋊D₉₁, …
maximal quotient of	D₉×C₇⋊D₉₁, C₃×D₃×C₇⋊D₉₁, D₃×C₃⋊(C₇⋊D₉₁), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 336);