Finite Group Databasebeta

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AGL(1,𝔽5)×#13049240 #72247575

order25920
automorphism?
homologyAbelianization (H1) = C33×C4 · Schur multiplier (H2) = C22×C32

Aliases

direct productAGL(1,𝔽5)×#13049240

Splittings

HallC24×AGL(1,𝔽5) ⋊ C3×3−1+2
SylowC5 ⋊ C4×#13049240

Subgroups

subgroupG/H
center, FrattiniC3C3×A42×AGL(1,𝔽5)
commutator, socleC24×C3×C5C33×C4
FittingC24×C32×C5C32×C4
prime radicalC32×D5×C22⋊A4C2×C3
cosocleC24×C3×D5C2×C33
hypercenterC32A42×AGL(1,𝔽5)
hypocenterC24×C5C3×C4×3−1+2
LCSG ▷ C24×C3×C5 ▷ C24×C5
UCSC1 ◁ C3 ◁ C32

2332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.