Finite Group Databasebeta

← Prev (#14295033) Next (#14295035) →

AGL(1,𝔽5)×(C2×D3)⋊C8 #14295034

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

Aliases

direct productAGL(1,𝔽5)×(C2×D3)⋊C8

Splittings

FittingC2×C3×C5×C8 ⋊ C2×C4
HallC3×C5 ⋊ C4×C22⋊C8
SylowC5 ⋊ C4×(C2×D3)⋊C8
SylowC3 ⋊ AGL(1,𝔽5)×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C4×C8
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C42
prime radicalC22×D3×D5C2×C4
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×C22⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20732);