Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 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:
2^6,17|a^2=e,e^2=f,b^a=bd,g^a=g^13,g^c=g^16,g^e=g^16104 conjugacy classes — view the full character table.
| maximal subgroup of | #14543621, #14543626, #14543646, … |
| maximal normal subgroup of | #14543621, #14543626, #14543646, … |
| maximal quotient of | #14544010, #14544013, #14544016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1517);