Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×#214 |
| Hall | C32×C7 ⋊ SD16 |
| Sylow | C32 ⋊ C7×SD16 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#63930, C3×D7×#214, #72245808, … |
| maximal normal subgroup of | C7×#63930, C3×D7×#214, #72245808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 438);