Finite Group Databasebeta

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#13013238

order1280
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

FittingC2×C5×C4⋊C8 ⋊ C4
SylowC5 ⋊ #7028

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C4×C8
FrattiniC2×C42C2×AGL(1,𝔽5)
FittingC2×C5×C4⋊C8C4
socleC23×C5#95
prime radicalC23×D5C22⋊C4
cosocleC2×C42×D5C22
hypercenterC2×C4⋊C8AGL(1,𝔽5)
hypocenterC5#7028
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=d,b^2=e,c^2=f,d^2=h,b^a=bc,c^a=cf,e^a=efg,c^b=cg,i^b=i^2,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, 1083506);