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#13017105

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

SylowC5 ⋊ #8235

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#8235
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

528 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=eg,d^2=g,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,c^b=ch,d^b=dh,i^b=i^2,i^f=i^4

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087373);