Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#3019 ⋊ C2 |
| Sylow | C5 ⋊ #33551 |
1326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|b^a=be,c^a=cf,g^a=gh,d^b=dh,f^b=fgh,i^b=i^4,e^c=eg,i^c=i^4,f^e=fh92 conjugacy classes — view the full character table.
| maximal subgroup of | #72243102, #72243135 |
| maximal normal subgroup of | D5×#33551, #72243102, #72243135 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 323627);