Finite Group Databasebeta

C3×#10600795 #14300356

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

Aliases

direct productC3×#10600795

Splittings

HallC3×C5 ⋊ #1868
SylowC5 ⋊ C3×#1868

Subgroups

subgroupG/H
centerC3×C4#4083
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#408C2
socleC2×C3×C5#385
prime radicalC2×C3×C5×#41C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#408D5
hypocenterC5C3×#1868
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#408

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 26054);