Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #88049⋊C3 |
| Fitting | C13×C4⋊C4 ⋊ C2×C3 |
| Hall | #88049 ⋊ C3 |
| Hall | C13⋊C3 ⋊ #102 |
| Sylow | C13 ⋊ C3×#102 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^2,3,2^3,13|b^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^12,e^b=ef,g^c=g^362 conjugacy classes — view the full character table.
| maximal subgroup of | #102×D13⋊C3, #72276135, #72276141 |
| maximal normal subgroup of | #102×D13⋊C3, #72276135, #72276141 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 20);