Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#18011884 |
| Fitting | C22×C22⋊C4×C149 ⋊ C2 |
| Sylow | C149 ⋊ C22×#121 |
2528 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9536 |
3016 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 17731);