Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #9954 |
1018 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^8,11|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fgh,i^a=i^10,c^b=cf,d^b=dg,e^b=eg,d^c=dh,e^c=eg227 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 70044);