Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C11×#491 ⋊ C2 |
| Sylow | C11 ⋊ #25584 |
1126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=h,b^2=h,c^2=f,d^2=eh,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^10,c^b=cg,g^b=gh,i^b=i^10,d^c=dh,g^c=gh,i^c=i^10206 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 222936);