Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 6144 |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | Dic3×C22⋊C4 |
| Sylow | C3 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(10,12)(13,14,15);(5,6,7,8)(9,10)(11,12);(1,2,3,4)(14,15)60 conjugacy classes — view the full character table.
| maximal subgroup of | #68952, #68955, Dic3×#99, … |
| maximal normal subgroup of | #68952, #68955, Dic3×#99, … |
| maximal quotient of | Dic3×#95, #69401, #69407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 500);