Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×#442 |
| Fitting | C3×#442 ⋊ C2 |
| Sylow | C3 ⋊ C2×#442 |
608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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:
(1,3,4,2)(6,10)(9,11)(13,14,15);(6,9)(7,12)(10,11);(1,2,4,3)(5,6,8,10)(7,9,12,11);(14,15)66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12439);