Finite Group Databasebeta

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#13015473

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

FittingC2×C5×C4⋊C8 ⋊ C4
SylowC5 ⋊ #7893

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC42C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC22×C5C2×#95
prime radicalC23×D5C22⋊C4
cosocleC42×D5C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5#7893
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=e,b^2=f,d^2=g,e^2=h,f^2=gh,b^a=bd,d^a=dg,f^a=fg,c^b=ch,i^b=i^2,i^f=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, 1085741);