Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | D3×H(3,ℤ/4) |
| Fitting | C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 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 — 3 generators on 19 points:
(1,3)(2,6,8,13)(4,10)(5,11)(7,9,14,15)(12,16)(17,18,19);(1,2)(3,9,11,15)(4,7)(5,8)(6,10,13,16)(12,14);(18,19)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1339, D3×#1340, #10705334, … |
| maximal normal subgroup of | D3×#1339, D3×#1340, #10705334, … |
| maximal quotient of | D3×#1274, #10684584, #10684587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1278);