Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 6144 |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | D3×#117 |
| Fitting | C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 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) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 15 points:
(5,7,8,11)(6,10,9,12)(13,14,15);(6,9)(10,12);(1,2,3,4)(5,6)(7,10)(8,9)(11,12);(14,15)60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×H(3,ℤ/4), D3×#339, #68753, … |
| maximal normal subgroup of | D3×H(3,ℤ/4), D3×#339, #68753, … |
| maximal quotient of | #73382, #73384, #73392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1079);