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AGL(1,𝔽5)×#508 #13043571

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#508

Splittings

FittingC5×#508 ⋊ C4
SylowC5 ⋊ C4×#508

Subgroups

subgroupG/H
centerC4D8×AGL(1,𝔽5)
commutatorC5×C8C23×C4
FrattiniC8C23×AGL(1,𝔽5)
FittingC5×#508C4
socleC2×C5C2×C4×D8
prime radicalD5×#508C2
cosocleC8×D5C24
hypercenter#508AGL(1,𝔽5)
hypocenterC5C4×#508
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2179, AGL(1,𝔽5)×#2263, AGL(1,𝔽5)×#1418
maximal normal subgroup ofAGL(1,𝔽5)×#2179, AGL(1,𝔽5)×#2263, AGL(1,𝔽5)×#1418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113839);