Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D17⋊#104 |
| Fitting | #41×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^6,17|a^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^13,d^b=df,g^c=g^16,g^e=g^1668 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#595, #14544549, #14544558, … |
| maximal normal subgroup of | #104×#595, #14544549, #14544558, … |
| maximal quotient of | #14544070, #14544073, #14544075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1544);