Finite Group Databasebeta

C3×#10599398 #14298706

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#10599398

Splittings

HallC3×C5 ⋊ #1831
SylowC5 ⋊ C3×#1831

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C22×C3×C8
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#336C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C4×C5C23×C3
hypercenterC3×#336D5
hypocenterC5C3×#1831
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×#336

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24404);