Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #88043⋊C3 |
| Hall | #88043 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #97 |
| Sylow | C13 ⋊ C3×#97 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^2,3,2^3,13|a^2=e,b^2=d,e^2=f,b^a=bf,g^a=g^12,g^c=g^392 conjugacy classes — view the full character table.
| maximal subgroup of | #97×D13⋊C3, #72276135 |
| maximal normal subgroup of | #97×D13⋊C3, #72276135 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 14);