Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#356 |
| Fitting | C3×#356 ⋊ C2 |
| Sylow | C3 ⋊ C2×#356 |
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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:
(1,3,6,5)(2,7,10,15)(4,13,14,12)(8,9,16,11)(17,18,19);(1,2,5,9,6,10,3,11)(4,8,12,15,14,16,13,7);(18,19)39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1405, #10715456, D3×#1410, … |
| maximal normal subgroup of | D3×#1405, #10715456, D3×#1410, … |
| maximal quotient of | D3×#1319, D3×#1325, #10704466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1746);