Finite Group Databasebeta

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AGL(1,𝔽5)×#64330 #72260264

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

Aliases

direct productAGL(1,𝔽5)×#64330

Splittings

FittingC23×C32×C5 ⋊ C22×C4
HallC32×C5 ⋊ C4×H(5,𝔽2)
SylowC32 ⋊ AGL(1,𝔽5)×H(5,𝔽2)
SylowC5 ⋊ C4×#64330

Subgroups

subgroupG/H
center, FrattiniC2C22×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C24×C4
FittingC23×C32×C5C22×C4
prime radicalD5×#64330C2
cosocleC2×C32×D5C25
hypercenterC23D32×AGL(1,𝔽5)
hypocenterC32×C5C4×H(5,𝔽2)
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C23

7066 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.