Finite Group Databasebeta

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D3×#1812 #10794825

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD3×#1812

Splittings

FittingC3×#1812 ⋊ C2
SylowC3 ⋊ C2×#1812

Subgroups

subgroupG/H
centerC4D3×#117
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1812C2
socleC2×C3C2×#380
prime radicalC2×D3×#41C22
cosocleC22×C3×C4C24
hypercenter#1812D3
hypocenterC3C2×#1812
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C2×M16 ◁ #1812

1346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#20788, D3×#12741, D3×#12873, …
maximal normal subgroup ofD3×#20788, D3×#12741, D3×#12873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 169206);