Finite Group Databasebeta

← Prev (#14416802) Next (#14416804) →

AGL(1,𝔽5)×#914 #14416803

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

Aliases

direct productAGL(1,𝔽5)×#914

Splittings

FittingC3×C5×SD16 ⋊ C2×C4
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ C4×#914
SylowC3 ⋊ AGL(1,𝔽5)×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×SD16C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#914C2
cosocleC3×C4×D5C24
hypercenterSD16D3×AGL(1,𝔽5)
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ SD16

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), AGL(1,𝔽5)×#63937, #72230912
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8)
maximal quotient ofAGL(1,𝔽5)×#63937, #72230912

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142501);