Finite Group Databasebeta

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#13021996

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

FittingC2×C5×C4⋊C8 ⋊ C4
SylowC5 ⋊ #10832

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×AGL(1,𝔽5)
commutatorC22×C5C2×C4×C8
FittingC2×C5×C4⋊C8C4
socleC23×C5C2×C42
prime radicalC23×D5C22×C4
cosocleC22×C4×D5C23
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5#10832
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=f,b^2=g,c^2=e,f^2=h,b^a=bd,c^a=ce,i^b=i^2,i^g=i^4

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1092264);