Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C27 · Schur multiplier (H2) = C23 |
| direct product | C22×D7⋊C27 |
| unambiguous semidirect product | D7⋊(C22×C27) |
| unambiguous semidirect product | (C7⋊C27)⋊C23 |
| unambiguous semidirect product | (C2×C7⋊C27)⋊C22 |
| derived, Sylow | C7 ⋊ C23×C27 |
| Hall | C7⋊C27 ⋊ C23 |
| Hall | C22×D7 ⋊ C27 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 756 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 86);