Finite Group Databasebeta

C3×#10603921 #14300367

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10603921

Splittings

HallC3×C5 ⋊ #1868
SylowC5 ⋊ C3×#1868

Subgroups

subgroupG/H
centerC2×C3#65699
commutatorC23×C5C22×C3×C4
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#99C4
socleC2×C3×C5#385
prime radicalC2×C3×#711C22
cosocleC22×Dic5C23×C3
hypercenterC3×#99AGL(1,𝔽5)
hypocenterC5C3×#1868
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#99

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26065);