Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D13⋊#208 |
| Hall | C3×C13 ⋊ C2×M16 |
| Sylow | C13 ⋊ C2×#208 |
| Sylow | C3 ⋊ D13⋊M16 |
136 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^5,3,13|a^2=d,b^2=e,d^2=e,c^a=ce,f^a=f^2,g^a=g^8,g^d=g^12108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1294);