Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#19098750 |
| Fitting | C4×H(5,𝔽2)×C79 ⋊ C2 |
| Sylow | C79 ⋊ C4×B(4,𝔽2) |
1910 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1910 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2528 |
2716 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 175550);