Finite Group Databasebeta

C3×#10603942 #14286704

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#10603942

Splittings

HallC3×C5 ⋊ #1583
SylowC5 ⋊ C3×#1583

Subgroups

subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#102C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×D4C2×C4
cosocleC4×Dic5C23×C3
hypercenterC3×#102AGL(1,𝔽5)
hypocenterC5C3×#1583
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 12402);