Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #21718 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×AGL(1,𝔽5) |
| commutator, socle, prime radical | C23×C5 | C23×C4 |
| Fitting | C5×#398 | C4 |
| cosocle | C22×Dic5 | C24 |
| hypercenter | #398 | AGL(1,𝔽5) |
| hypocenter | C5 | #21718 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #398 | |
774 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=e,c^2=f,d^2=eg,g^2=h,b^a=be,c^a=cf,i^a=i^3,c^b=ch,i^b=i^4,d^c=dh,i^d=i^2,i^g=i^498 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1107163);