Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#88237 |
| Fitting | C2×C3×C4×C13 ⋊ C4 |
| Hall | C3×C13 ⋊ #117 |
| Sylow | C13 ⋊ C3×#117 |
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 312 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,8,11,15,9,13,14,6,10,16,12,7)(18,22)(21,24);(17,19,20,23)(18,21,22,24);(5,6,7,9)(8,11,12,16)(10,14,15,13)(17,18)(19,21)(20,22)(23,24)132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1284);