Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D3×#490 |
| Fitting | C3×#490 ⋊ C2 |
| Sylow | C3 ⋊ C2×#490 |
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,6)(5,8)(9,11,12,10,14,15,13,16)(17,18,19);(1,3,4,7)(2,5,6,8)(9,10,12,15,14,16,13,11);(1,2)(3,5)(4,6)(7,8)(10,15)(11,16)(12,13);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1355, D3×#1412, D3×#1656, … |
| maximal normal subgroup of | D3×#1355, D3×#1412, D3×#1656, … |
| maximal quotient of | D3×#1836, D3×#1936, D3×#1961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14288);