Finite Group Databasebeta

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AGL(1,𝔽5)×#64312 #72231724

order5760
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#64312

Splittings

FittingC32×C5×D4 ⋊ C22×C4
HallC32×C5 ⋊ C2×C4×#41
SylowC32 ⋊ C2×#41×AGL(1,𝔽5)
SylowC5 ⋊ C4×#64312

Subgroups

subgroupG/H
center, FrattiniC2C22×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C24×C4
FittingC32×C5×D4C22×C4
prime radicalD5×#64312C2
cosocleC2×C32×D5C25
hypercenterD4D32×AGL(1,𝔽5)
hypocenterC32×C5C2×C4×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ D4

7338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.