Finite Group Databasebeta

C3×#10603867 #14285772

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

Aliases

direct productC3×#10603867

Splittings

HallC3×C5 ⋊ #1569
SylowC5 ⋊ C3×#1569

Subgroups

subgroupG/H
centerC22×C3C2×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#97C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C4⋊C4
cosocleC4×Dic5C23×C3
hypercenterC3×#97AGL(1,𝔽5)
hypocenterC5C3×#1569
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#97

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, 11470);