Finite Group Databasebeta

C3×#10603861 #14280374

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

Aliases

direct productC3×#10603861

Splittings

HallC3×C5 ⋊ C8×M16
SylowC5 ⋊ C3×C8×M16

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#97C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C42
cosocleC4×Dic5C23×C3
hypercenterC3×#97AGL(1,𝔽5)
hypocenterC5C3×C8×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×#97

448 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, 6072);