Finite Group Databasebeta

← Prev (#72221460) Next (#72221462) →

AGL(1,𝔽5)×#3288 #72221461

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

Aliases

direct productAGL(1,𝔽5)×#3288

Splittings

FittingC5×#3288 ⋊ C4
SylowC5 ⋊ C4×#3288

Subgroups

subgroupG/H
centerC2D42×AGL(1,𝔽5)
commutatorC2×C4×C5C24×C4
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC5×#3288C4
socleC2×C5C4×D42
prime radicalD5×#3288C2
cosocleC2×C4×D5C25
hypercenter#3288AGL(1,𝔽5)
hypocenterC5C4×#3288
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #3288

5150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#61110
maximal normal subgroup ofAGL(1,𝔽5)×#61110

GAP

Past the SmallGroups library coverage — no SmallGroups id.