Finite Group Databasebeta

C3×#10603806 #14280336

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#10603806

Splittings

HallC3×C5 ⋊ C2×#322
SylowC5 ⋊ C2×C3×#322

Subgroups

subgroupG/H
centerC3×C42C2×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C42
cosocleC4×Dic5C23×C3
hypercenterC3×C4×C8AGL(1,𝔽5)
hypocenterC5C2×C3×#322
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C42 ◁ C3×C4×C8

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6034);