Finite Group Databasebeta

C3×#10603775 #14295156

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×#10603775

Splittings

HallC3×C5 ⋊ C8×C22⋊C4
SylowC5 ⋊ C3×C8×C22⋊C4

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC22×Dic5C23×C3
hypercenterC3×#95AGL(1,𝔽5)
hypocenterC5C3×C8×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

768 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20854);