Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C4⋊C8×C13⋊C3 |
| unambiguous semidirect product | C4⋊(C8×C13⋊C3) |
| unambiguous semidirect product | (C13×C4⋊C8)⋊C3 |
| Fitting, Hall | C13×C4⋊C8 ⋊ C3 |
| Sylow | C13 ⋊ C3×C4⋊C8 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 25 points:
(2,4)(5,6,7,9,8,10,11,12)(14,15,17)(16,19,22)(18,21,20)(23,25,24);(1,2,3,4)(13,14,16,15,18,22,19,23,25,17,20,24,21)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 128);