Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #88135⋊C3 |
| Fitting | C13×C22⋊C4 ⋊ C2×C3 |
| Hall | #88135 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C4×D4 |
| Sylow | C13 ⋊ C3×C4×D4 |
188 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 75 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|c^2=e,b^a=bf,g^a=g^12,c^b=cf,g^d=g^980 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4×D13⋊C3 |
| maximal normal subgroup of | C4×D4×D13⋊C3 |
| maximal quotient of | #72276142 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 359);