Finite Group Databasebeta

← Prev (#72242517) Next (#72242519) →

AGL(1,𝔽5)×#3060 #72242518

order2560
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#3060

Splittings

FittingC5×#3060 ⋊ C4
SylowC5 ⋊ C4×#3060

Subgroups

subgroupG/H
centerC22C22×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C24×C4
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#3060C4
socleC22×C5C22×C4×D4
prime radicalD5×#3060C2
cosocleC2×C4×D5C25
hypercenter#3060AGL(1,𝔽5)
hypocenterC5C4×#3060
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3060

5680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72269234
maximal quotient of#72269234

GAP

Past the SmallGroups library coverage — no SmallGroups id.