Finite Group Databasebeta

← Prev (#72269503) Next (#72269505) →

C2×C3×#10591522 #72269504

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×#10591522

Splittings

FittingC22×C33×D4 ⋊ C22
SylowC33 ⋊ C2×#453

Subgroups

subgroupG/H
centerC22×C3#63983
commutator, cosocleC2×C32×C4C24×C3
FrattiniC2×C4C22×C3×D32
FittingC22×C33×D4C22
socleC22×C33#120
hypercenterC22×C3×D4D32
hypocenterC32C2×C3×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

4706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.