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#13014654

order1280
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

SylowC5 ⋊ #7570

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#7570
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Polycyclic presentation:

2^8,5|a^2=e,b^2=f,c^2=fgh,d^2=g,e^2=h,b^a=bd,d^a=df,i^a=i^2,d^b=dg,e^b=efg,i^e=i^4

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1084922);