Finite Group Databasebeta

C3×#10603894 #14280569

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#10603894

Splittings

HallC3×C5 ⋊ #1452
SylowC5 ⋊ C3×#1452

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×C5C42
cosocleC4×Dic5C23×C3
hypercenterC3×C22⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1452
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C22⋊C8

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6267);