Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| unambiguous semidirect product | #88237⋊C3 |
| Fitting | C2×C4×C13 ⋊ C3×C4 |
| Hall | #88237 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #117 |
| Sylow | C13 ⋊ C3×#117 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 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,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 | #72229029, #41×AGL(1,𝔽13), #72229055, … |
| maximal normal subgroup of | #72229029, #41×AGL(1,𝔽13), #72229055, … |
| maximal quotient of | #72259385, #72259390, #72259525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1160);