Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | D3×#338 |
| Fitting | C3×#338 ⋊ C2 |
| Sylow | C3 ⋊ C2×#338 |
372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 372 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 — 3 generators on 19 points:
(1,3,5,12,6,13,4,11)(2,7,8,10,9,16,14,15)(17,18,19);(1,2,4,8,6,9,5,14)(3,10,12,7,13,15,11,16);(18,19)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1341, D3×#1342, #10705347, … |
| maximal normal subgroup of | D3×#1341, D3×#1342, #10705347, … |
| maximal quotient of | D3×#1275, #10684604, #10684607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1296);