Finite Group Databasebeta

C3×#10604741 #14312647

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

Aliases

direct productC3×#10604741

Splittings

HallC3×C5 ⋊ #2108
SylowC5 ⋊ C3×#2108

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×M16C4
socleC22×C3×C5C22×C8
prime radicalC23×C3×C5C2×C8
cosocleC2×#168C23×C3
hypercenterC2×C3×M16AGL(1,𝔽5)
hypocenterC5C3×#2108
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M16

368 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, 38345);