Finite Group Databasebeta

← Prev (#14276795) Next (#14276797) →

C3×#10598589 #14276796

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

Aliases

direct productC3×#10598589

Splittings

FittingC3×C5×C4⋊C8 ⋊ C4
HallC3×C5 ⋊ #1279
SylowC5 ⋊ C3×#1279

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C3×C4×C8
FrattiniC42C2×C3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C8C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C22⋊C4
cosocleC42×D5C22×C3
hypercenterC3×C4⋊C8AGL(1,𝔽5)
hypocenterC5C3×#1279
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4⋊C8

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2494);