Finite Group Databasebeta

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#13028032

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

No aliases for this group.

Splittings

FittingC4×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ #13818

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC4×C5×C4⋊C4C4
socleC23×C5C23×C4
prime radical, cosocleC23×D5C24
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#13818
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4

1690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=g,b^2=h,c^2=eg,d^2=fg,b^a=be,c^a=cf,d^b=de,i^b=i^2,i^h=i^4

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098300);