Finite Group Databasebeta

C3×#10604185 #14298714

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

Aliases

direct productC3×#10604185

Splittings

HallC3×C5 ⋊ #1831
SylowC5 ⋊ C3×#1831

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C22×C3×C8
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC2×C3×C42×C5C4
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×Dic5C23×C3
hypercenterC2×C3×C42AGL(1,𝔽5)
hypocenterC5C3×#1831
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24412);