Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ C4×#368 |
314 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=e,b^2=f,c^2=deg,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,d^b=dg,e^b=eg,g^b=gh,i^c=i^10308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 84979);