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#13044455

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

No aliases for this group.

Splittings

FittingC2×C5×H(5,𝔽2) ⋊ C4
SylowC5 ⋊ #60070

Subgroups

subgroupG/H
centerC2C23×C22⋊AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×H(5,𝔽2)C4
socleC2×C5C23×C22⋊C4
prime radicalC2×#66285C2
cosocleC22×D5C25
hypercenterC2×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5#60070
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×#41 ◁ C2×H(5,𝔽2)

4892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Polycyclic presentation:

2^8,5|a^2=g,e^2=h,b^a=bf,f^a=fh,i^a=i^2,g^b=gh,d^c=dh,i^e=i^4,i^g=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, 1114723);