Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#359 |
| Fitting | C3×#359 ⋊ C2 |
| Sylow | C3 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 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)(2,8)(4,17)(5,14)(6,22)(7,15)(9,26)(10,23)(11,25)(12,16)(13,19)(18,30)(20,32)(21,24)(27,28)(29,31)(33,34,35);(1,2,5,10,7,11,6,21)(3,12,14,28,15,29,22,26)(4,16,18,27,20,31,19,9)(8,17,23,30,25,32,24,13);(34,35)66 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#359, D3×#2143, #10948117, … |
| maximal normal subgroup of | C2×D3×#359, D3×#2143, #10948117, … |
| maximal quotient of | D3×#1331, D3×#1332, #10704924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1816);