Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #21827 |
1130 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 235 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,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=ce,d^b=dh,i^b=i^10,g^c=gh206 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 179020);