Finite Group Databasebeta

← Prev (#72258387) Next (#72258389) →

AGL(1,𝔽5)×#12310 #72258388

order5120
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽5)×#12310

Splittings

FittingC5×#12310 ⋊ C4
SylowC5 ⋊ C4×#12310

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#1619
commutatorC4×C5×C8C23×C4
FrattiniC4×C8C23×AGL(1,𝔽5)
FittingC5×#12310C4
socleC2×C5C4×#1619
prime radicalD5×#12310C2
cosocleC4×C8×D5C24
hypercenter#12310AGL(1,𝔽5)
hypocenterC5C4×#12310
LCSG ▷ C4×C5×C8 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #12310

4162 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.