Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C16 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×C79⋊C16 |
| derived, Sylow | C79 ⋊ C22×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C8 | D79 |
| commutator, hypocenter | C79 | C22×C4×C16 |
| Frattini | C2×C8 | C23×D79 |
| Fitting | C22×C4×C8×C79 | C2 |
| socle, prime radical | C24×C79 | C2×C8 |
| cosocle | C2×C8×C79 | C24 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C22×C4×C8 | |
1022 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20224 |
5248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 322191);