Finite Group Databasebeta

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AGL(1,𝔽5)×#3006 #72258397

order2560
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productAGL(1,𝔽5)×#3006

Splittings

FittingC5×#3006 ⋊ C4
SylowC5 ⋊ C4×#3006

Subgroups

subgroupG/H
centerC22C22×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C24×C4
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#3006C4
socleC22×C5C22×C4×D4
prime radicalD5×#3006C2
cosocleC2×C4×D5C25
hypercenter#3006AGL(1,𝔽5)
hypocenterC5C4×#3006
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

10616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.