Finite Group Databasebeta

← Prev (#14295009) Next (#14295011) →

C3×AGL(1,𝔽5)×C22⋊C8 #14295010

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×AGL(1,𝔽5)×C22⋊C8

Splittings

FittingC3×C5×C22⋊C8 ⋊ C4
HallC3×C5 ⋊ C4×C22⋊C8
SylowC5 ⋊ C3×C4×C22⋊C8

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C2×C3×C4×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×D5C2×C4
cosocleC2×C4×D5C23×C3
hypercenterC3×C22⋊C8AGL(1,𝔽5)
hypocenterC5C3×C4×C22⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C22⋊C8

872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 20708);