Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#1157 |
| Fitting | C2×C32×C4×C7 ⋊ C2 |
| Hall | C32×C7 ⋊ #41 |
| Sylow | C7 ⋊ C32×#41 |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 504 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3)(7,8,10,12,13,11,9)(15,19)(18,21);(4,5,6)(14,16,17,20)(15,18,19,21);(8,9)(10,11)(12,13)(14,15)(16,18)(17,19)(20,21)306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 829);