Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (D13⋊C3)⋊M16 |
| unambiguous semidirect product | (D13⋊M16)⋊C3 |
| Hall | D13⋊M16 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×M16 |
| Sylow | C13 ⋊ C2×C3×M16 |
136 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^3,3,2^2,13|a^2=e,b^2=f,e^2=f,c^a=cf,g^a=g^8,g^d=g^9,g^e=g^1268 conjugacy classes — view the full character table.
| maximal subgroup of | #72229101, #72229103, #72229106, … |
| maximal normal subgroup of | #72229101, #72229103, #72229106, … |
| maximal quotient of | #72229279, #72259343, #72275914 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1157);