Finite Group Databasebeta

C2×D3×M16×C3⋊D3 #72243322

order3456
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C3

Aliases

direct productC2×D3×M16×C3⋊D3

Splittings

FittingC2×C33×M16 ⋊ C22
SylowC33 ⋊ C23×M16

Subgroups

subgroupG/H
centerC2×C4C22×D3×C3⋊D3
commutatorC2×C33C24×C4
FrattiniC4C23×D3×C3⋊D3
FittingC2×C33×M16C22
socleC22×C33C23×C4
prime radicalC23×D3×C3⋊D3C4
cosocleC33×C4C25
hypercenterC2×M16D3×C3⋊D3
hypocenterC33C23×M16
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C2×M16

11512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.