Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#350 |
| Fitting | C3×#350 ⋊ C2 |
| Sylow | C3 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,3)(2,8)(4,17)(5,19)(6,14)(7,16)(9,25)(10,27)(11,13)(12,24)(15,21)(18,31)(20,22)(23,29)(26,30)(28,32)(33,34,35);(1,2,5,10,6,11,20,28,7,12,21,29,4,9,18,26)(3,13,15,30,14,24,31,27,16,25,19,32,17,8,22,23);(34,35)84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#350, D3×#2117, #10947891, … |
| maximal normal subgroup of | C2×D3×#350, D3×#2117, #10947891, … |
| maximal quotient of | D3×#1315, #10704260, D3×#1323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1700);