Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#456 |
| Fitting | C3×#456 ⋊ C2 |
| Sylow | C3 ⋊ C2×#456 |
708 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 135 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 — 4 generators on 19 points:
(1,4,6,2)(3,10,12,7)(5,8,15,13)(9,14,16,11)(17,18,19);(1,3)(2,7)(4,10)(5,14)(6,12)(8,16)(9,13)(11,15);(1,2,6,4)(3,9,12,16)(5,13,15,8)(7,14,10,11);(18,19)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1405, #10715456, D3×#2203, … |
| maximal normal subgroup of | D3×#1405, #10715456, D3×#2203, … |
| maximal quotient of | D3×#1603, D3×#1609, D3×#1604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12873);