Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#23900 (order 3072) · Inn(G) = C22×D3 · Out(G) = C2×D42 |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×M16 |
| Fitting | C2×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C22×M16 |
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(1,2)(3,4,5)(7,10)(11,13);(6,7,8,11,9,10,12,13);(4,5);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×H(3,ℤ/4), D3×#338, D3×#339, … |
| maximal normal subgroup of | D3×H(3,ℤ/4), D3×#338, D3×#339, … |
| maximal quotient of | C2×#4701, #78482, C2×D3×#97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1302);