Finite Group Databasebeta

C3×#10600542 #14294234

order1920
automorphism?
homologyAbelianization (H1) = C3×C43 · Schur multiplier (H2) = C2×C42

Aliases

direct productC3×#10600542

Splittings

HallC3×C5 ⋊ #1726
SylowC5 ⋊ C3×#1726

Subgroups

subgroupG/H
centerC22×C3×C8C2×D5
commutatorC2×C5C3×C43
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×C8D5
hypocenterC5C3×#1726
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C8 ◁ C2×C3×C4×C8

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19932);