Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×Q8×C13 ⋊ C4 |
| Hall | C3×C13 ⋊ #103 |
| Sylow | C13 ⋊ #835 |
| Sylow | C3 ⋊ #88117 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^5,3,13|a^2=c,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^8,d^b=de,g^c=g^1269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 492);