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AGL(1,𝔽5)×#510 #13043577

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

Aliases

direct productAGL(1,𝔽5)×#510

Splittings

FittingC5×#510 ⋊ C4
SylowC5 ⋊ C4×#510

Subgroups

subgroupG/H
centerC2C2×D8×AGL(1,𝔽5)
commutatorC5×C8C23×C4
FrattiniC8C23×AGL(1,𝔽5)
FittingC5×#510C4
socleC2×C5C2×C4×D8
prime radicalD5×#135C22
cosocleC8×D5C24
hypercenter#510AGL(1,𝔽5)
hypocenterC5C4×#510
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113845);