Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×#3633 |
| Fitting | C17×#127 ⋊ C8 |
| Sylow | C17 ⋊ C8×#127 |
1350 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 289 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #127×AGL(1,𝔽17), #453×#3633, #72242849 |
| maximal normal subgroup of | #127×AGL(1,𝔽17), #453×#3633, #72242849 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1118165);