Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #13737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×AGL(1,𝔽5) |
| commutator, socle | C2×C5 | C22×C32 |
| Fitting | C5×M64 | C4 |
| prime radical | #709 | C16 |
| cosocle | #3926 | C23 |
| hypercenter | M64 | AGL(1,𝔽5) |
| hypocenter | C5 | #13737 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C16 ◁ M64 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^2,c^b=ch,i^b=i^4,i^d=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098150);