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AGL(1,𝔽5)×#1426 #72242156

order2560
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productAGL(1,𝔽5)×#1426

Splittings

FittingC5×#1426 ⋊ C4
SylowC5 ⋊ C4×#1426

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#367
commutatorC5×C16C2×C42
FrattiniC2×C16C22×AGL(1,𝔽5)
FittingC5×#1426C4
socleC2×C5C4×#367
prime radicalC22×D5C2×SD32
cosocleC2×D5×C16C23
hypercenter#1426AGL(1,𝔽5)
hypocenterC5C4×#1426
LCSG ▷ C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

416 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 subgroup ofAGL(1,𝔽5)×#13658
maximal normal subgroup ofAGL(1,𝔽5)×#13658

GAP

Past the SmallGroups library coverage — no SmallGroups id.