Finite Group Databasebeta

← Prev (#14416034) Next (#14416036) →

D3×D8×AGL(1,𝔽5) #14416035

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD3×D8×AGL(1,𝔽5)

Splittings

FittingC3×C5×D8 ⋊ C2×C4
HallC3×C5 ⋊ C2×C4×D8
SylowC5 ⋊ C4×D3×D8
SylowC3 ⋊ C2×D8×AGL(1,𝔽5)

Subgroups

subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD3×D5×D8C2
cosocleC3×C4×D5C24
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×D8
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ D8

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), AGL(1,𝔽5)×#63926, D3×#13104055, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), C2×D3×D8×AGL(1,𝔽5)
maximal quotient ofAGL(1,𝔽5)×#63926, D3×#13104055, C2×D3×D8×AGL(1,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141733);