Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×Q8⋊C8 ⋊ C2 |
| Sylow | C17 ⋊ #1494 |
230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cg,d^b=df,h^b=h^16,h^c=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1494, C2×#14527243, #17000934, … |
| maximal normal subgroup of | D17×#1494, C2×#14527243, #17000934, … |
| maximal quotient of | #16922655, #16922660, #16922665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2969);