Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | D42×Dic79 |
| Sylow | C79 ⋊ C4×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D79 |
| commutator | C22×C79 | C24×C4 |
| Fitting, prime radical | C2×D42×C79 | C2 |
| socle, cosocle | C23×C79 | C25 |
| hypercenter | C2×D42 | D79 |
| hypocenter | C79 | C4×D42 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×D42 | |
4804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
2050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 329358);