Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#6129 |
| Fitting | C2×C3×D4×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C2×#41 |
| Sylow | C13 ⋊ C2×C3×#41 |
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 624 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1387);