Finite Group Databasebeta

C22×D3×D4×C3⋊D3 #72243236

order3456
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215×C3

Aliases

direct productC22×D3×D4×C3⋊D3

Splittings

FittingC22×C33×D4 ⋊ C22
SylowC33 ⋊ C24×D4

Subgroups

subgroupG/H
centerC23C22×D3×C3⋊D3
commutator, cosocleC2×C33C26
FrattiniC2C24×D3×C3⋊D3
FittingC22×C33×D4C22
socleC23×C33C24
hypercenterC22×D4D3×C3⋊D3
hypocenterC33C24×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C23 ◁ C22×D4

68760 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.