Finite Group Databasebeta

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AGL(1,𝔽5)×#1555 #72258352

order2560
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productAGL(1,𝔽5)×#1555

Splittings

FittingC5×#1555 ⋊ C4
SylowC5 ⋊ C4×#1555

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×AGL(1,𝔽5)
commutatorC2×C4×C5C22×C42
FrattiniC42C23×AGL(1,𝔽5)
FittingC5×#1555C4
socleC22×C5C2×C4×C22⋊C4
prime radicalC2×D5×#127C22
cosocleC42×D5C24
hypercenter#1555AGL(1,𝔽5)
hypocenterC5C4×#1555
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

3716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal quotient ofAGL(1,𝔽5)×#11992

GAP

Past the SmallGroups library coverage — no SmallGroups id.