Finite Group Databasebeta

C3×#10598122 #14276955

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

Aliases

direct productC3×#10598122

Splittings

HallC3×C5 ⋊ #1286
SylowC5 ⋊ C3×#1286

Subgroups

subgroupG/H
centerC22×C3#3963
commutatorC2×C4×C5C3×C42
FrattiniC2×C42C2×C3×D5
FittingC3×C5×#382C2
socleC22×C3×C5#95
prime radicalC23×C3×C5C22⋊C4
cosocleC2×C42×C5C22×C3
hypercenterC3×#382D5
hypocenterC5C3×#1286
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#382

312 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, 2653);