Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×B(4,𝔽2) (order 768) · Inn(G) = D3×C22⋊C4 · Out(G) = C23 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×#99 |
| Fitting | C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(1,2,3)(4,6)(5,8)(7,11)(9,10);(4,5)(6,10,11,8)(7,9);(2,3)33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AΣL(1,𝔽16), #69135, D3×#352, … |
| maximal normal subgroup of | D3×AΣL(1,𝔽16), #69135, D3×#352, … |
| maximal quotient of | D3×#323, #68119, #68120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 302);