Finite Group Databasebeta

C3×#10605888 #14327264

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

Aliases

direct productC3×#10605888

Splittings

HallC3×C5 ⋊ #2351
SylowC5 ⋊ C3×#2351

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#382C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC3×#382D5
hypocenterC5C3×#2351
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#382

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52962);