Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C5×#2646 ⋊ C2 |
| Sylow | C5 ⋊ #36750 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2646 | C2 |
| prime radical | C24×D5 | C23 |
| hypercenter | #2646 | D5 |
| hypocenter | C5 | #36750 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2646 | |
1778 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=fg,c^2=g,d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^4,c^b=ch,d^b=dfh,i^b=i^4,i^c=i^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 377232);