Finite Group Databasebeta

C3×#10620277 #14520116

order1968
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10620277

Splittings

HallC3×C41 ⋊ M16
SylowC41 ⋊ C3×M16

Subgroups

subgroupG/H
centerC3×C4C2×D41
commutatorC2×C41C2×C3×C4
FrattiniC4C2×C3×D41
FittingC2×C3×C4×C41C2
socleC2×C3×C41C2×C4
prime radicalC22×C3×C41C4
cosocleC4×C41C22×C3
hypercenterC2×C3×C4D41
hypocenterC41C3×M16
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 39);