Finite Group Databasebeta

← Prev (#72249296) Next (#72249298) →

D3×#60369 #72249297

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productD3×#60369

Splittings

FittingC3×#60369 ⋊ C2
SylowC3 ⋊ C2×#60369

Subgroups

subgroupG/H
centerC22C23×D3×D4
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC3×#60369C2
socleC22×C3C24×D4
hypercenter#60369D3
hypocenterC3C2×#60369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×#41 ◁ #60369

45588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#449496, D3×#10576108
maximal normal subgroup ofD3×#449496, D3×#10576108
maximal quotient ofD3×#6453969

GAP

Past the SmallGroups library coverage — no SmallGroups id.