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#13034304

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

FittingC23×C5×C8 ⋊ C4
SylowC5 ⋊ #20658

Subgroups

subgroupG/H
centerC2×C4C2×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC23×C5×C8C4
socleC22×C5C22×C4⋊C4
prime radicalC24×D5D4
cosocleC2×C4×D5C24
hypercenterC23×C8AGL(1,𝔽5)
hypocenterC5#20658
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8

1646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Polycyclic presentation:

2^8,5|a^2=g,b^2=e,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=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, 1104572);