Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#509 |
| Fitting | C3×#509 ⋊ C2 |
| Sylow | C3 ⋊ C2×#509 |
400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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 — 4 generators on 19 points:
(2,7)(6,14)(8,15)(9,13)(17,18,19);(2,6)(3,10)(4,11)(7,14)(8,9)(12,16)(13,15);(1,2)(3,6)(4,13)(5,7)(8,10)(9,11)(12,14)(15,16);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,ℤ/16), #10948658, D3×#2190, … |
| maximal normal subgroup of | D3×AGL(1,ℤ/16), #10948658, D3×#2190, … |
| maximal quotient of | D3×#2140, D3×#2139, D3×#2159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14610);