Finite Group Databasebeta

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D3×#2955 #11659486

order768
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD3×#2955

Splittings

FittingC3×#2955 ⋊ C2
SylowC3 ⋊ C2×#2955

Subgroups

subgroupG/H
centerC8C2×D3×D4
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC3×#2955C2
socleC2×C3C22×C4×D4
prime radicalD3×#575C2
cosocleC2×C3×C4C25
hypercenter#2955D3
hypocenterC3C2×#2955
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2955

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#60184, D3×#21559, D3×#33692, …
maximal normal subgroup ofD3×#60184, D3×#21559, D3×#33692, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1033867);