Finite Group Databasebeta

C3×#10615731 #14418120

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10615731

Splittings

HallC3×C5 ⋊ #2956
SylowC5 ⋊ C3×#2956

Subgroups

subgroupG/H
centerC3×C4C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC3×C5×#575C2
socleC2×C3×C5C2×C4×D4
cosocleC2×C4×C5C24×C3
hypercenterC3×#575D5
hypocenterC5C3×#2956
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#575

916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 143818);