Finite Group Databasebeta

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D3×#2961 #11659554

order768
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productD3×#2961

Splittings

FittingC3×#2961 ⋊ C2
SylowC3 ⋊ C2×#2961

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2961C2
prime radicalC23×D3C22×C4
cosocleC2×C3×C4C25
hypercenter#2961D3
hypocenterC3C2×#2961
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2961

1894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#60207, D3×#61414, D3×#61378, …
maximal normal subgroup ofD3×#60207, D3×#61414, D3×#61378, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1033935);