Finite Group Databasebeta

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D3×#72224662 #72269715

order12288
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productD3×#72224662

Splittings

FittingC3×#72224662 ⋊ C2
SylowC3 ⋊ C2×#72224662

Subgroups

subgroupG/H
centerC2D3×#72224639
commutatorC3×C32C23×C16
Frattini#7330C23×D3
FittingC3×#72224662C2
socleC2×C3C2×#72224639
prime radicalD3×#13742C8
cosocleC3×#7330C24
hypercenter#72224662D3
hypocenterC3C2×#72224662
LCSG ▷ C3×C32 ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1311 ◁ #93668 ◁ #72224662

2070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

285 conjugacy classes. The character table is too large to display.

Relationships

holomorph ofC3×C64

GAP

Past the SmallGroups library coverage — no SmallGroups id.