Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×Q8×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C22⋊Q8 |
| Sylow | C13 ⋊ #946 |
| Sylow | C3 ⋊ #88200 |
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 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|b^2=e,c^2=e,c^a=cd,f^a=f^2,g^a=g^12,c^b=ce204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1120);