Finite Group Databasebeta

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D3×#72224639 #72245237

order6144
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productD3×#72224639

Splittings

FittingC3×#72224639 ⋊ C2
SylowC3 ⋊ C2×#72224639

Subgroups

subgroupG/H
centerC22D3×#12067
commutatorC3×C16C23×C16
Frattini#1311C23×D3
FittingC3×#72224639C2
socleC22×C3C2×#12067
prime radicalC2×D3×D32C8
cosocleC3×#1311C24
hypercenter#72224639D3
hypocenterC3C2×#72224639
LCSG ▷ C3×C16 ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #7053 ◁ #72224639

1888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1536

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#72224662
maximal normal subgroup ofD3×#72224662
maximal quotient ofD3×#72224662

GAP

Past the SmallGroups library coverage — no SmallGroups id.