Finite Group Databasebeta

← Prev (#72243018) Next (#72243020) →

AGL(1,𝔽5)×#12705 #72243019

order5120
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productAGL(1,𝔽5)×#12705

Splittings

FittingC5×#12705 ⋊ C4
SylowC5 ⋊ C4×#12705

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#1781
commutatorC24×C5C22×C42
FrattiniC22×D4C23×AGL(1,𝔽5)
FittingC5×#12705C4
socleC2×C5C4×#1781
prime radicalD5×#3484C22
cosocleC22×D4×D5C24
hypercenter#12705AGL(1,𝔽5)
hypocenterC5C4×#12705
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #12705

16522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#511790
maximal normal subgroup ofAGL(1,𝔽5)×#511790

GAP

Past the SmallGroups library coverage — no SmallGroups id.