Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#1272 ⋊ C2 |
| Sylow | C11 ⋊ #7617 |
550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=e,b^2=f,c^2=h,d^2=g,e^2=h,b^a=bd,c^a=ch,d^a=df,d^b=dg,e^b=efg,i^b=i^10,i^c=i^10242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 57750);