Finite Group Databasebeta

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AGL(1,𝔽5)×#2883 #72269814

order2560
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productAGL(1,𝔽5)×#2883

Splittings

FittingC5×#2883 ⋊ C4
SylowC5 ⋊ C4×#2883

Subgroups

subgroupG/H
centerC2C22×C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C23×C42
FrattiniC23C24×AGL(1,𝔽5)
FittingC5×#2883C4
socleC2×C5C22×C4×C22⋊C4
prime radicalC2×D5×H(5,𝔽2)C22
cosocleC23×D5C25
hypercenter#2883AGL(1,𝔽5)
hypocenterC5C4×#2883
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×D4 ◁ #2883

11050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

205 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#60399, AGL(1,𝔽5)×#23996, AGL(1,𝔽5)×#21776
maximal normal subgroup ofAGL(1,𝔽5)×#60399, AGL(1,𝔽5)×#23996, AGL(1,𝔽5)×#21776

GAP

Past the SmallGroups library coverage — no SmallGroups id.