Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×D4×C13 ⋊ C22 |
| Hall | C3×C13 ⋊ C2×D8 |
| Sylow | C13 ⋊ D3×D8 |
| Sylow | C3 ⋊ D8×D13 |
152 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 312 |
Polycyclic presentation:
2^5,3,13|d^2=e,c^a=cd,d^a=de,g^a=g^12,c^b=cd,d^b=de,f^b=f^2,d^c=de93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 734);