Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C79 · Schur multiplier (H2) = C29 |
| direct product | C79×#7555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C79 | C23 |
| commutator | C23 | C2×C42×C79 |
| Frattini, cosocle | C25 | C23×C79 |
| prime radical | C26×C79 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C79 ◁ G | |
4566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
6952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 543);