Finite Group Databasebeta

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#13022502

order1280
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC2×C5×AGL(1,ℤ/8) ⋊ C4
SylowC5 ⋊ #11034

Subgroups

subgroupG/H
centerC2#10604954
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×AGL(1,ℤ/8)C4
socleC2×C5#1438
prime radicalC2×D5×AGL(1,ℤ/8)C2
cosocleC22×C4×D5C23
hypercenterC2×AGL(1,ℤ/8)AGL(1,𝔽5)
hypocenterC5#11034
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Polycyclic presentation:

2^8,5|a^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,i^a=i^2,c^b=cf,f^b=fh,g^b=gh,d^c=dh,f^c=fh,g^c=gh,i^g=i^4

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1092770);