Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×#349 ⋊ C2 |
| Sylow | C17 ⋊ #2190 |
226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^16,d^b=df,e^b=eg,f^b=fg,h^b=h^16,d^c=dg196 conjugacy classes — view the full character table.
| maximal subgroup of | #16946490, #16946491, #16946502, … |
| maximal normal subgroup of | #16946490, #16946491, #16946502, … |
| maximal quotient of | #16946423, #16946428, #16946434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6458);