Finite Group Databasebeta

C3×#10600860 #14298656

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

Aliases

direct productC3×#10600860

Splittings

HallC3×C5 ⋊ #1829
SylowC5 ⋊ C3×#1829

Subgroups

subgroupG/H
centerC2×C3#65232
commutatorC23×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#100C2
socleC2×C3×C5#381
prime radicalC22×C3×C5×D4C22
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#100D5
hypocenterC5C3×#1829
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24354);