Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×C11×Q16 ⋊ C2 |
| Sylow | C11 ⋊ #17856 |
678 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=f,b^2=g,c^2=fg,e^2=g,f^2=h,b^a=be,d^a=dg,e^a=eg,e^b=eg,d^c=dg,i^d=i^10368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 139037);