Finite Group Databasebeta

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AGL(1,𝔽5)×#2433 #72258307

order2560
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4

Aliases

direct productAGL(1,𝔽5)×#2433

Splittings

FittingC5×#2433 ⋊ C4
SylowC5 ⋊ C4×#2433

Subgroups

subgroupG/H
center, FrattiniC23C24×AGL(1,𝔽5)
commutator, socleC23×C5C24×C4
FittingC5×#2433C4
prime radicalD5×#2433C2
cosocleC23×D5C25
hypercenter#2433AGL(1,𝔽5)
hypocenterC5C4×#2433
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2433

18172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.