Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 3072 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#823 |
| Fitting | C2×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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 — 3 generators on 13 points:
(3,4,5)(6,7,8,11,9,10,12,13);(4,5)(7,10)(8,12);(1,2)42 conjugacy classes — view the full character table.
| maximal subgroup of | #68705, #68706, #68722, … |
| maximal normal subgroup of | #68705, #68706, #68722, … |
| maximal quotient of | C2×#4464, #69798, #69859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 689);