Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#333 |
| Fitting | C3×#333 ⋊ C2 |
| Sylow | C3 ⋊ C2×#333 |
256 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 256 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,5)(3,7)(9,10,12,14)(11,16,15,13)(17,18,19);(1,2,3,6,4,5,7,8)(10,13)(11,15)(14,16);(18,19)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1405, C2×D3×#333, D3×#1542, … |
| maximal normal subgroup of | D3×#1405, C2×D3×#333, D3×#1542, … |
| maximal quotient of | D3×#1272, #10683167, #10683474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1056);