Finite Group Databasebeta

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AGL(1,𝔽5)×#2912 #72253184

order2560
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productAGL(1,𝔽5)×#2912

Splittings

FittingC5×#2912 ⋊ C4
SylowC5 ⋊ C4×#2912

Subgroups

subgroupG/H
centerC22C22×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C42
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#2912C4
socleC22×C5C22×C4×D4
prime radicalC2×D5×#41C23
cosocleC2×C4×D5C25
hypercenter#2912AGL(1,𝔽5)
hypocenterC5C4×#2912
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2912

6456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.