Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊#1055) |
| Hall | C3×C13 ⋊ C4⋊C8 |
| Sylow | C13 ⋊ C4⋊(C3⋊C8) |
| Sylow | C3 ⋊ C4⋊#1055 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1248 |
Polycyclic presentation:
2^5,3,13|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^2,g^a=g^12324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 228);