Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C13 ⋊ #124 |
| Sylow | C13 ⋊ #936 |
| Sylow | C3 ⋊ #88129 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|b^2=d,c^2=de,b^a=be,c^a=cde,g^a=g^12,f^b=f^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 557);