Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| unambiguous semidirect product | #88139⋊C3 |
| Fitting | C13×C22⋊C4 ⋊ C2×C3 |
| Hall | #88139 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #124 |
| Sylow | C13 ⋊ C3×#124 |
152 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^3,3,2^2,13|a^2=f,c^2=f,b^a=bf,c^a=cf,g^a=g^12,c^b=ce,g^d=g^962 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 356);