Finite Group Databasebeta

C3×#10615513 #14411520

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#10615513

Splittings

HallC3×C5 ⋊ #2875
SylowC5 ⋊ C3×#2875

Subgroups

subgroupG/H
centerC2×C3×C4C23×D5
commutatorC2×C5C22×C3×C42
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#131C2
socleC22×C3×C5C23×C4
prime radicalC2×C3×C5×#41C22
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#131D5
hypocenterC5C3×#2875
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#131

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137218);