Finite Group Databasebeta

← Prev (#72230310) Next (#72230312) →

C32×AGL(1,𝔽5)×#120 #72230311

order5760
automorphism?
homologyAbelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C27×C3

Aliases

direct productC32×AGL(1,𝔽5)×#120

Splittings

FittingC32×C5×#120 ⋊ C4
HallC32×C5 ⋊ C4×#120
SylowC5 ⋊ C32×C4×#120

Subgroups

subgroupG/H
centerC22×C32C23×AGL(1,𝔽5)
commutatorC22×C5C23×C32×C4
FrattiniC22C23×C32×AGL(1,𝔽5)
FittingC32×C5×#120C4
socleC22×C32×C5C23×C4
prime radicalC32×D5×#120C2
cosocleC22×D5C24×C32
hypercenterC32×#120AGL(1,𝔽5)
hypocenterC5C32×C4×#120
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C32×#120

7344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×AGL(1,𝔽5)×#120
maximal normal subgroup ofC3⋊D3×AGL(1,𝔽5)×#120

GAP

Past the SmallGroups library coverage — no SmallGroups id.