Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#88138 |
| Fitting | C3×C13×C22⋊C4 ⋊ C2 |
| Hall | C3×C13 ⋊ #121 |
| Sylow | C13 ⋊ C3×#121 |
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 624 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,9,11,13,15,16,14,12,10,8,6)(18,20)(21,22)(23,24);(17,18,19,20)(22,24);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(22,24)222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 887);