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#13028073

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

FittingC4×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ #13846

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
prime radical, cosocleC23×D5C24
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#13846
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=h,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,i^a=i^2,c^b=cg,i^h=i^4

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098341);