Finite Group Databasebeta

← Prev (#72247478) Next (#72247480) →

A4×AGL(1,𝔽5)×3−1+2 #72247479

order6480
automorphism?
homologyAbelianization (H1) = C33×C4 · Schur multiplier (H2) = C2×C32

Aliases

direct productA4×AGL(1,𝔽5)×3−1+2

Splittings

FittingC22×C5×3−1+2 ⋊ C3×C4
HallC22×AGL(1,𝔽5) ⋊ C3×3−1+2
SylowC5 ⋊ C4×A4×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×A4×AGL(1,𝔽5)
commutator, socleC22×C3×C5C33×C4
FittingC22×C5×3−1+2C3×C4
prime radicalC32×D5×A4C2×C3
cosocleC22×C3×D5C2×C33
hypercenter3−1+2A4×AGL(1,𝔽5)
hypocenterC22×C5C3×C4×3−1+2
LCSG ▷ C22×C3×C5 ▷ C22×C5
UCSC1 ◁ C3 ◁ 3−1+2

568 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#13049240, A4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×S4×3−1+2, …
maximal normal subgroup ofA4×AGL(1,𝔽5)×AGL(1,ℤ/9), AGL(1,𝔽5)×S4×3−1+2, AGL(1,𝔽5)×A4⋊AGL(1,ℤ/9)
maximal quotient ofAGL(1,𝔽5)×#13049240

GAP

Past the SmallGroups library coverage — no SmallGroups id.