Finite Group Databasebeta

C3×#10599968 #14315362

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

Aliases

direct productC3×#10599968

Splittings

HallC3×C5 ⋊ C4×SD32
SylowC5 ⋊ C3×C4×SD32

Subgroups

subgroupG/H
centerC22×C3D5×D8
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×C5×D8C22
cosocleC2×C5×C8C23×C3
hypercenterC3×#357D5
hypocenterC5C3×C4×SD32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#357

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 41060);