Finite Group Databasebeta

← Prev (#14320334) Next (#14320336) →

C2×#11751933 #14320335

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#11751933
unambiguous semidirect productD5⋊#4665

Splittings

FittingC22×C3×C4×C5 ⋊ C2×C4
HallC3×C5 ⋊ C2×#386
SylowC5 ⋊ C2×#4665
SylowC3 ⋊ C2×#65779

Subgroups

subgroupG/H
centerC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC22×D5×D12C2
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

3152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46033);