Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C5×#2276 ⋊ C2 |
| Sylow | C5 ⋊ C4×#519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator | C2×C5 | C23×C42 |
| Fitting | C5×#2276 | C2 |
| socle, cosocle | C23×C5 | C25 |
| prime radical | C23×D5 | C24 |
| hypercenter | #2276 | D5 |
| hypocenter | C5 | C4×#519 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2276 | |
3402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,d^2=f,e^2=fg,b^a=bf,d^a=df,c^b=cf,i^c=i^4,i^e=i^4272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 327818);