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D3×#2143 #10948112

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×#2143

Splittings

FittingC3×#2143 ⋊ C2
SylowC3 ⋊ C2×#2143

Subgroups

subgroupG/H
centerC4C2×D3×D8
commutatorC3×C8C23×C4
FrattiniC2×C8C23×D3
FittingC3×#2143C2
socleC2×C3C22×#102
prime radicalC2×D3×#135C2
cosocleC2×C3×C8C24
hypercenter#2143D3
hypocenterC3C2×#2143
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

1154 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×#33463, D3×#12649, D3×#12743, …
maximal normal subgroup ofD3×#33463, D3×#12649, D3×#12743, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322493);