Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#480 |
| Fitting | C3×#480 ⋊ C2 |
| Sylow | C3 ⋊ C2×#480 |
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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:
(1,3,4,7)(2,6,5,8)(10,13)(11,16)(14,15)(17,18,19);(2,5)(6,8);(1,2)(3,6)(4,5)(7,8)(9,10)(11,13)(12,15)(14,16);(18,19)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1607, D3×#1609, D3×#1610, … |
| maximal normal subgroup of | D3×#1607, D3×#1609, D3×#1610, … |
| maximal quotient of | D3×#1823, D3×#1852, D3×#1874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13856);