Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×#327 |
| Fitting | C3×#327 ⋊ C2 |
| Sylow | C3 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(1,3)(2,5)(4,8)(6,7)(10,13)(11,16)(14,15)(17,18,19);(1,2)(3,7,8,5)(4,6)(9,10)(11,13)(12,15)(14,16);(18,19)57 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#327, D3×#1500, D3×#1501, … |
| maximal normal subgroup of | C2×D3×#327, D3×#1500, D3×#1501, … |
| maximal quotient of | D3×#1270, D3×#1271, #10683143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 876);