Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×Dic3⋊C8 |
| unambiguous semidirect product | Dic3⋊(C8×C13) |
| Hall | C3×C13 ⋊ C4⋊C8 |
| Sylow | C3 ⋊ C13×C4⋊C8 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1248 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(18,20)(21,22,23,25,24,26,27,28);(15,16)(17,18,19,20)468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 197);