Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C13×C22⋊C4 ⋊ C2 |
| Hall | C3×C13 ⋊ #124 |
| Sylow | C13 ⋊ #885 |
| Sylow | C3 ⋊ #88139 |
152 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 624 |
Polycyclic presentation:
2^5,3,13|a^2=e,c^2=e,b^a=be,c^a=ce,f^a=f^2,g^a=g^12,c^b=cd204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1053);