Finite Group Databasebeta

← Prev (#14416657) Next (#14416659) →

C4×C5×#914 #14416658

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC4×C5×#914

Splittings

FittingC3×C4×C5×SD16 ⋊ C2
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC3 ⋊ C4×C5×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#914C2
cosocleC2×C3×C4C24×C5
hypercenterC4×C5×SD16D3
hypocenterC3C4×C5×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C4×C5×SD16

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142356);