Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#2956 ⋊ C2 |
| Sylow | C11 ⋊ #33688 |
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^8,11|d^2=e,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^10,f^b=fh,d^c=dg,e^c=eh,f^c=fg,g^c=gh,f^d=fh254 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#33688, #72269607, #72269643 |
| maximal normal subgroup of | D11×#33688, #72269607, #72269643 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 324800);