Finite Group Databasebeta

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D3×#83937 #72252602

order2304
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productD3×#83937

Splittings

FittingC2×C32×AGL(1,ℤ/8) ⋊ C22
SylowC32 ⋊ C2×#3151

Subgroups

subgroupG/H
centerC22C2×D32×D4
commutator, cosocleC2×C32×C4C25
FrattiniC2×C4C23×D32
FittingC2×C32×AGL(1,ℤ/8)C22
socleC22×C32C23×D4
hypercenterC2×AGL(1,ℤ/8)D32
hypocenterC32C2×#3151
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

8228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×#3151
maximal normal subgroup ofD32×#3151

GAP

Past the SmallGroups library coverage — no SmallGroups id.