Finite Group Databasebeta

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D3×#1386 #10710100

order768
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD3×#1386

Splittings

FittingC3×#1386 ⋊ C2
SylowC3 ⋊ C2×#1386

Subgroups

subgroupG/H
centerC22D3×#102
commutatorC3×C8C2×C42
FrattiniC22×C8C22×D3
FittingC3×#1386C2
socleC22×C3C2×#102
prime radicalC23×D3D8
cosocleC22×C3×C8C23
hypercenter#1386D3
hypocenterC3C2×#1386
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

630 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×#12956, D3×#12647, D3×#13001, …
maximal normal subgroup ofD3×#12956, D3×#12647, D3×#13001, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 84481);