Finite Group Databasebeta

C3×#10620279 #14520118

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

Aliases

direct productC3×#10620279

Splittings

HallC3×C41 ⋊ C4⋊C4
SylowC41 ⋊ C3×C4⋊C4

Subgroups

subgroupG/H
centerC22×C3C2×D41
commutatorC2×C41C2×C3×C4
FrattiniC22C2×C3×D41
FittingC2×C3×C4×C41C2
socle, prime radicalC22×C3×C41C22
cosocleC22×C41C22×C3
hypercenterC2×C3×C4D41
hypocenterC41C3×C4⋊C4
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1968

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, 41);