Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×AΣL(1,𝔽16) |
| Fitting | C3×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C3 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(1,2,3)(5,8)(9,10);(4,5)(6,10,11,8)(7,9);(2,3)39 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×AΣL(1,𝔽16), D3×#2120, D3×#2121, … |
| maximal normal subgroup of | C2×D3×AΣL(1,𝔽16), D3×#2120, D3×#2121, … |
| maximal quotient of | D3×#1316, D3×#1326, #10704434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1710);