Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#3712 |
| Hall | C32×C7 ⋊ M16 |
| Sylow | C32 ⋊ C7×M16 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#63818, D7×#3712, #72245724, … |
| maximal normal subgroup of | C7×#63818, D7×#3712, #72245724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 346);