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D3×#3147 #11664601

order768
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productD3×#3147

Splittings

FittingC3×#3147 ⋊ C2
SylowC3 ⋊ C2×#3147

Subgroups

subgroupG/H
centerC2×C4C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3147C2
socleC22×C3C23×D4
hypercenter#3147D3
hypocenterC3C2×#3147
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3147

3366 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×#33717, D3×#19603, D3×#21706, …
maximal normal subgroup ofD3×#33717, D3×#19603, D3×#21706, …
maximal quotient ofD3×#19603

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1038982);