Finite Group Databasebeta

C3×Dic5×#99 #14295370

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×Dic5×#99

Splittings

HallC3×C5 ⋊ C4×#99
SylowC5 ⋊ C3×C4×#99

Subgroups

subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC22×C5C2×C3×C42
FrattiniC24C22×C3×D5
FittingC2×C3×C5×#99C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C22
cosocleC24×C5C23×C3
hypercenterC2×C3×#99D5
hypocenterC5C3×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#99

824 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, 21068);