Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#798 |
| Fitting | C3×C13×C16 ⋊ C2 |
| Hall | C3×C13 ⋊ M32 |
| Sylow | C3 ⋊ C13×M32 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 624 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,18,19,23,20,24,25,30,21,22,26,28,27,29,31,32);(15,16)(18,22)(23,28)(24,29)(30,32)468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 181);