Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×#354 |
| Fitting | C3×#354 ⋊ C2 |
| Sylow | C3 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 284 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:
(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(17,18,19);(1,2)(3,9,11,16)(4,12,14,7)(5,8)(6,10)(13,15);(18,19)39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1404, #10715440, D3×#1406, … |
| maximal normal subgroup of | D3×#1404, #10715440, D3×#1406, … |
| maximal quotient of | D3×#1319, D3×#1324, #10704462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1732);