Finite Group Databasebeta

← Prev (#14276821) Next (#14276823) →

C3×#10598821 #14276822

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10598821

Splittings

HallC3×C5 ⋊ #1280
SylowC5 ⋊ C3×#1280

Subgroups

subgroupG/H
centerC23×C3C22⋊AGL(1,𝔽5)
commutatorC22×C5C3×C4×C8
FrattiniC24C2×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC23×C3×C5C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC23×Dic5C22×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C3×#1280
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C24×C3 ◁ C23×C3×C4

528 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, 2520);