Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | D3×#364 |
| Fitting | C3×#364 ⋊ C2 |
| Sylow | C3 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(1,3,4,13,7,14,6,5)(2,8,9,12,11,10,15,16)(17,18,19);(1,2,5,10,6,9,14,16,7,11,13,8,4,15,3,12);(18,19)84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1335, #10704972, D3×#1336, … |
| maximal normal subgroup of | D3×#1335, #10704972, D3×#1336, … |
| maximal quotient of | D3×#1367, #10706730, D3×#1370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1878);