Finite Group Databasebeta

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AGL(1,𝔽5)×#2901 #72258444

order2560
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productAGL(1,𝔽5)×#2901

Splittings

FittingC5×#2901 ⋊ C4
SylowC5 ⋊ C4×#2901

Subgroups

subgroupG/H
centerC4C22×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C42
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#2901C4
socleC2×C5C22×C4×C22⋊C4
prime radicalD5×#585C22
cosocleC2×C4×D5C25
hypercenter#2901AGL(1,𝔽5)
hypocenterC5C4×#2901
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2901

10416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.