Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#329 |
| Fitting | C3×#329 ⋊ C2 |
| Sylow | C3 ⋊ C2×#329 |
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,5)(3,7)(9,10)(11,15)(12,14)(13,16)(17,18,19);(1,2,3,6,4,5,7,8)(10,13,14,15);(18,19)57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1403, D3×#1404, C2×D3×#329, … |
| maximal normal subgroup of | D3×#1403, D3×#1404, C2×D3×#329, … |
| maximal quotient of | D3×#1270, D3×#1272, #10683153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 916);