Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×#368 |
| Fitting | C3×#368 ⋊ C2 |
| Sylow | C3 ⋊ C2×#368 |
144 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,3,13,29,6,16,20,30,7,17,19,22,5,15,4,14)(2,8,18,27,10,23,25,28,11,24,32,31,21,26,9,12)(33,34,35);(1,2,5,10,7,11,6,21)(3,12,15,27,17,28,16,31)(4,18,19,25,20,32,13,9)(8,22,23,30,24,29,26,14);(34,35)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1417, #10715640, D3×#1419, … |
| maximal normal subgroup of | D3×#1417, #10715640, D3×#1419, … |
| maximal quotient of | D3×#1371, D3×#1372, #10706769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1935);