Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#3797 |
| Hall | C32×C7 ⋊ C2×Q8 |
| Sylow | C32 ⋊ C2×C7×Q8 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3797, C7×#64306, #72245742, … |
| maximal normal subgroup of | D7×#3797, C7×#64306, #72245742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 756);