Finite Group Databasebeta

← Prev (#72258447) Next (#72258449) →

AGL(1,𝔽5)×#33688 #72258448

order5120
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,𝔽5)×#33688

Splittings

FittingC5×#33688 ⋊ C4
SylowC5 ⋊ C4×#33688

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#3109
commutatorC2×C5×C8C24×C4
FrattiniC2×C8C24×AGL(1,𝔽5)
FittingC5×#33688C4
socleC2×C5C4×#3109
prime radicalD5×#33688C2
cosocleC2×C8×D5C25
hypercenter#33688AGL(1,𝔽5)
hypocenterC5C4×#33688
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #33688

6898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.