Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | D3×#347 |
| Fitting | C3×#347 ⋊ C2 |
| Sylow | C3 ⋊ C2×#347 |
168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,6,8,9)(3,10)(7,15,16,14)(11,13)(17,18,19);(1,2,3,7,4,9,11,15,5,8,10,16,12,6,13,14);(18,19)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1355, D3×#1356, #10706362, … |
| maximal normal subgroup of | D3×#1355, D3×#1356, #10706362, … |
| maximal quotient of | D3×#1313, #10704186, #10704228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1662);