Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#1057 |
| Hall | C3×C13 ⋊ C22⋊C8 |
| Sylow | C13 ⋊ (C2×D3)⋊C8 |
| Sylow | C3 ⋊ C22⋊#1057 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|a^2=c,c^2=e,b^a=bd,g^a=g^8,f^b=f^2,g^c=g^1272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 329);