Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#466 |
| Fitting | C3×#466 ⋊ C2 |
| Sylow | C3 ⋊ C2×#466 |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(2,4)(13,14,15);(5,6,10,12,8,11,7,9);(1,2)(3,4)(6,9)(7,10)(11,12);(14,15)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1347, #10705422, D3×#1349, … |
| maximal normal subgroup of | D3×#1347, #10705422, D3×#1349, … |
| maximal quotient of | D3×#1667, D3×#1673, D3×#1681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13289);