Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#932 |
| Fitting | C2×C3×D4×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ AGL(1,ℤ/8) |
| Sylow | C3 ⋊ C13×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(18,23)(19,20)(22,24);(17,19,21,20)(18,22,24,23);(15,16)(17,18)(19,22)(20,23)(21,24)273 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1025);