Finite Group Databasebeta

C3×#10602470 #14300689

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10602470

Splittings

HallC3×C5 ⋊ #1874
SylowC5 ⋊ C3×#1874

Subgroups

subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
Fitting, prime radicalC2×C3×C5×#121C2
socleC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#121D5
hypocenterC5C3×#1874
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26387);