Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Q8×C13⋊C3 |
| Fitting, Hall | C4×Q8×C13 ⋊ C3 |
| Sylow | C13 ⋊ C3×C4×Q8 |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4)(14,15,17)(16,19,22)(18,21,20)(23,25,24);(5,6,7,8)(9,12,11,10)(13,14,16,15,18,22,19,23,25,17,20,24,21);(5,9,7,11)(6,10,8,12)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 836);