Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×C4⋊C8 ⋊ C2 |
| Sylow | C17 ⋊ #435 |
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^b=g^16,g^c=g^16188 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#435, C2×#11762879, #14537473, … |
| maximal normal subgroup of | D17×#435, C2×#11762879, #14537473, … |
| maximal quotient of | #14527612, #14527619, #14527626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 619);