Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | D4×C7⋊C27 |
| unambiguous semidirect product | C4⋊(C2×C7⋊C27) |
| unambiguous semidirect product | (C7×D4)⋊C27 |
| Hall | C7×D4 ⋊ C27 |
| Sylow | C7 ⋊ D4×C27 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 756 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4)(6,7,8)(9,11,10)(12,13,16,14,17,22,19,24,29,15,18,23,20,25,30,27,32,35,21,26,31,28,33,36,34,37,38);(2,4)(5,6,7,9,8,10,11)225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 20);