Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C7⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C7⋊(Q8⋊C9) |
| unambiguous semidirect product | (C3×C7)⋊(Q8⋊C9) |
| unambiguous semidirect product | (C3×Q8)⋊(C7⋊C9) |
| derived, Hall | C7×Q8 ⋊ C3×C9 |
| Sylow | Q8 ⋊ C3×C7⋊C9 |
| Sylow | C7 ⋊ C3×Q8⋊C9 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1512 |
153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 336);