Finite Group Databasebeta

← Prev (#26039681) Next (#26039683) →

D₃×C₁₃×#3862 #26039682

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	D₃×C₁₃×#3862
unambiguous semidirect product	C₃⋊(C₂×C₁₃×#3862)

Splittings

Fitting, socle	C₃×C₇²×C₁₃ ⋊ C₂×C₃
derived	C₃×C₇² ⋊ C₂×C₃×C₁₃
Hall	C₃×C₁₃×#3862 ⋊ C₂
Hall	C₇²×C₁₃ ⋊ C₃×D₃
Hall	C₃×#3862 ⋊ C₂×C₁₃
Sylow	C₇² ⋊ C₃×D₃×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₃×#3862
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₃

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

741 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₁₃×#64418, D₃×C₁₃⋊#64418, D₃×C₁₃×#64422, …
maximal normal subgroup of	D₃×C₁₃×#64418, D₃×C₁₃⋊#64418, D₃×C₁₃×#64422, …
maximal quotient of	Dic₃×C₁₃×#3862, C₂×D₃×C₁₃×#3862

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 325);