Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | D4×#4427 |
| unambiguous semidirect product | C4⋊(C2×#4427) |
| Fitting | C7×D4×C9 ⋊ C3 |
| Hall | C7×D4 ⋊ 3−1+2 |
| Sylow | C7 ⋊ D4×3−1+2 |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 252 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4)(5,6,7,9,8,10,11)(12,13,16,14,15,19,17,18,20);(2,4)(6,7,8)(9,11,10)(13,15,18)(16,20,19)145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 315);