Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×D181⋊M16 |
| unambiguous semidirect product | D181⋊(C22×M16) |
| Sylow | C181 ⋊ C23×M16 |
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5792 |
1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 21496);