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#13016154

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

Aliases

No aliases for this group.

Splittings

FittingC4×C5×M16 ⋊ C4
SylowC5 ⋊ #8028

Subgroups

subgroupG/H
centerC2×C4(C2×AGL(1,𝔽5))⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC42C22×AGL(1,𝔽5)
FittingC4×C5×M16C4
socleC22×C5C2×#95
prime radicalC23×D5C22⋊C4
cosocleC42×D5C23
hypercenterC4×M16AGL(1,𝔽5)
hypocenterC5#8028
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=e,b^2=f,c^2=g,d^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fgh,i^a=i^2,d^b=dh,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, 1086422);