Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C23×D3×#120 (order 1536) · Inn(G) = C22×D3 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D3×C22⋊C8 |
| Fitting | C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(2,4)(13,14,15);(1,2)(3,4)(5,6,7,9,8,10,11,12);(14,15)60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#323, #68119, #68122, … |
| maximal normal subgroup of | D3×#323, #68119, #68122, … |
| maximal quotient of | #68100, #68101, D3×#323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 283);