Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#458 |
| Fitting | C3×#458 ⋊ C2 |
| Sylow | C3 ⋊ C2×#458 |
794 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 794 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) = 48 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,7)(5,10)(6,12)(8,14)(9,15)(11,17)(13,19)(16,18);(4,6)(5,9)(7,12)(8,13)(10,15)(11,16)(14,19)(17,18);(4,5,8,11)(6,9,13,16)(7,10,14,17)(12,18,19,15);(2,3)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2197, D3×#2198, D3×#2200, … |
| maximal normal subgroup of | D3×#2197, D3×#2198, D3×#2200, … |
| maximal quotient of | D3×#1607, D3×#1613, D3×#1608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12886);