Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#23765403 |
| Fitting | C2×#354×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#2199 |
1392 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1392 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2528 |
1048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 323599);