Finite Group Databasebeta

C3×#10599574 #14295740

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#10599574

Splittings

HallC3×C5 ⋊ C4×#103
SylowC5 ⋊ C3×C4×#103

Subgroups

subgroupG/H
centerC23×C3D4×D5
commutatorC4×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#340C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC3×#340D5
hypocenterC5C3×C4×#103
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21438);