Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D3×AGL(1,ℤ/8) |
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 5 generators on 13 points:
(1,2)(3,4,5)(7,11)(10,12);(7,10)(8,13)(11,12);(6,7)(8,10)(9,11)(12,13);(4,5);(1,2)66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19764);