Finite Group Databasebeta

C3×#10598701 #14278743

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

Aliases

direct productC3×#10598701

Splittings

HallC3×C5 ⋊ #1377
SylowC5 ⋊ C3×#1377

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C3×C4×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socleC22×C3×C5C22⋊C8
prime radicalC23×C3×C5C2×C8
cosocleC22×#168C22×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C3×#1377
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×C42

280 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, 4441);