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AGL(1,𝔽5)×#2263 #72242152

order2560
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#2263

Splittings

FittingC5×#2263 ⋊ C4
SylowC5 ⋊ C4×#2263

Subgroups

subgroupG/H
centerC2C2×AGL(1,𝔽5)×D16
commutatorC5×C16C23×C4
FrattiniC16C23×AGL(1,𝔽5)
FittingC5×#2263C4
socleC2×C5C2×C4×D16
prime radicalD5×#2263C2
cosocleD5×C16C24
hypercenter#2263AGL(1,𝔽5)
hypocenterC5C4×#2263
LCSG ▷ C5×C16 ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

928 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.