Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×#131 |
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ C22×#131 |
1504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 5 generators on 21 points:
(1,2)(3,4,5)(6,8)(7,11)(9,15)(10,14)(12,18)(13,17)(16,20)(19,21);(8,14)(11,17)(15,20)(18,21);(6,7,9,12,10,13,16,19)(8,11,15,18,14,17,20,21);(4,5);(1,2)120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19734);