Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×D42 (order 768) · Inn(G) = C2×D3×D4 · Out(G) = C23 |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×AGL(1,ℤ/8) |
| Fitting | C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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 — 4 generators on 11 points:
(2,6)(5,7)(9,10,11);(2,5)(3,8)(6,7);(1,2)(3,5)(4,6)(7,8);(10,11)33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#453, #80279, D3×#454, … |
| maximal normal subgroup of | D3×#453, #80279, D3×#454, … |
| maximal quotient of | #78866, #78870, #78878, … |
| automorphism group of | D24, Dic12 |
| holomorph of | C3×C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1331);