Finite Group Databasebeta

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D3×#1957 #10798809

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

Aliases

direct productD3×#1957

Splittings

FittingC3×#1957 ⋊ C2
SylowC3 ⋊ C2×#1957

Subgroups

subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1957C2
socleC23×C3C22×D4
prime radicalC2×D3×#127C2
cosocleC22×C3×C4C24
hypercenter#1957D3
hypocenterC3C2×#1957
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

2414 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×#21690, D3×#9837, D3×#8977
maximal normal subgroup ofD3×#21690, D3×#9837, D3×#8977
maximal quotient ofD3×#9837, D3×#13213, D3×#13210

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 173190);