Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#346 |
| Fitting | C3×#346 ⋊ C2 |
| Sylow | C3 ⋊ C2×#346 |
200 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4)(6,10)(11,16)(12,17)(18,20)(21,22,23);(5,6,7,11,8,12,13,18,9,10,14,16,15,17,19,20);(22,23)120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1313, #10704190, #10704194, … |
| maximal normal subgroup of | D3×#1313, #10704190, #10704194, … |
| maximal quotient of | D3×#1311, D3×#1312, #10704203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1646);