Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#492 |
| Fitting | C3×#492 ⋊ C2 |
| Sylow | C3 ⋊ C2×#492 |
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 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) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3,4)(13,14,15);(5,6,7,9,8,10,11,12);(2,4)(6,9)(7,11)(10,12);(14,15)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1359, D3×#1409, D3×#1410, … |
| maximal normal subgroup of | D3×#1359, D3×#1409, D3×#1410, … |
| maximal quotient of | D3×#1705, D3×#1706, D3×#1707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14335);