Finite Group Databasebeta

← Prev (#72242088) Next (#72242090) →

AGL(1,𝔽5)×#1398 #72242089

order2560
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C42

Aliases

direct productAGL(1,𝔽5)×#1398

Splittings

FittingC5×#1398 ⋊ C4
SylowC5 ⋊ C4×#1398

Subgroups

subgroupG/H
centerC8C42×AGL(1,𝔽5)
commutatorC4×C5C42×C8
FrattiniC2×C16C22×AGL(1,𝔽5)
FittingC5×#1398C4
socleC2×C5C4×#346
prime radicalC22×D5C2×M32
cosocleC2×D5×C16C23
hypercenter#1398AGL(1,𝔽5)
hypocenterC5C4×#1398
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C8 ◁ #1398

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#7333, AGL(1,𝔽5)×#7457, AGL(1,𝔽5)×#13658, …
maximal normal subgroup ofAGL(1,𝔽5)×#7333, AGL(1,𝔽5)×#7457, AGL(1,𝔽5)×#13658, …
maximal quotient of#72242271, #72269175

GAP

Past the SmallGroups library coverage — no SmallGroups id.