Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#1828 ⋊ C2 |
| Sylow | C5 ⋊ #21776 |
1520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=ce,f^b=fh,g^b=gh,i^b=i^4,i^c=i^4,g^d=gh104 conjugacy classes — view the full character table.
| maximal subgroup of | #72253568, D5×#21776 |
| maximal normal subgroup of | #72253568, D5×#21776 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 178719);