Finite Group Databasebeta

C2×C3×#65224 #14320128

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

Aliases

direct productC2×C3×#65224

Splittings

HallC3×C5 ⋊ C2×#384
SylowC5 ⋊ C2×C3×#384

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C42×C5C2
socle, prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC22×C3×C42D5
hypocenterC5C2×C3×#384
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C42

1776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45826);