Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 24576 |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#929 |
| Fitting | C23×C3×C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#123 |
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7)(8,9)(10,12,13,16)(11,15,14,17);(1,2)(10,11)(12,15)(13,14)(16,17);(4,5)(7,9)(11,14)(15,17);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #69535, #69538, #69539, … |
| maximal normal subgroup of | #69535, #69538, #69539, … |
| maximal quotient of | C2×#4933, C2×#4940, C4×#929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1348);