Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#23771443 |
| Fitting | C2×#383×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#2818 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D79 |
| commutator, cosocle | C23×C79 | C25 |
| Frattini | C23 | C24×D79 |
| Fitting | C2×#383×C79 | C2 |
| socle | C24×C79 | C24 |
| hypercenter | C2×#383 | D79 |
| hypocenter | C79 | C2×#2818 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ C2×#383 | |
3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10112 |
2236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 376123);