Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C27 |
| direct product | C2×D149⋊(C22⋊C8) |
| unambiguous semidirect product | D149⋊(C2×C22⋊C8) |
| Sylow | C149 ⋊ C22×C22⋊C8 |
1072 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 306 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4768 |
1264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 21084);