Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D3×#498 |
| Fitting | C3×#498 ⋊ C2 |
| Sylow | C3 ⋊ C2×#498 |
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(9,10,11,13,12,14,15,16)(17,18,19);(1,3,4,8)(2,5,6,7);(1,2,4,6)(3,7,8,5)(10,13)(11,15)(14,16);(18,19)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1654, D3×#1651, D3×#1653, … |
| maximal normal subgroup of | D3×#1654, D3×#1651, D3×#1653, … |
| maximal quotient of | D3×#1844, D3×#1941, D3×#1990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14466);