Finite Group Databasebeta

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AGL(1,𝔽5)×#3805 #72230248

order2880
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#3805

Splittings

HallC32×C5 ⋊ C4×#41
SylowC32 ⋊ #41×AGL(1,𝔽5)
SylowC5 ⋊ C4×#3805

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC22×C32×C5C22×C4
prime radicalD5×#3805C2
cosocleC2×C32×D5C24
hypercenterC22D32×AGL(1,𝔽5)
hypocenterC32×C5C4×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

1348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#64306, AGL(1,𝔽5)×#64330, #72260281
maximal normal subgroup ofAGL(1,𝔽5)×#64306, AGL(1,𝔽5)×#64330, #72260281

GAP

Past the SmallGroups library coverage — no SmallGroups id.