Finite Group Databasebeta

C3×#10598152 #14276834

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#10598152

Splittings

HallC3×C5 ⋊ #1281
SylowC5 ⋊ C3×#1281

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊Dic5
commutatorC22×C5C3×C4×C8
FrattiniC2×C42C2×C3×D5
FittingC2×C3×C5×#97C2
socleC22×C3×C5#95
prime radicalC23×C3×C5C42
cosocleC2×C42×C5C22×C3
hypercenterC2×C3×#97D5
hypocenterC5C3×#1281
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×#97

304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2532);