Finite Group Databasebeta

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D3×#93759 #72254963

order3072
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD3×#93759

Splittings

FittingC3×#93759 ⋊ C2
SylowC3 ⋊ C2×#93759

Subgroups

subgroupG/H
centerC4D3×#1333
commutatorC3×C16C22×C16
Frattini#1311C22×D3
FittingC3×#93759C2
socleC2×C3C2×#7070
prime radicalD3×#508C8
cosocleC3×#1311C23
hypercenter#93759D3
hypocenterC3C2×#93759
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C16 ◁ #1311 ◁ #93759

746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72224647
maximal normal subgroup ofD3×#72224647

GAP

Past the SmallGroups library coverage — no SmallGroups id.