Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C42×D173 |
| Fitting | C22×C42×C173 ⋊ C2 |
| derived, Sylow | C173 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D173 |
| commutator, hypocenter | C173 | C23×C42 |
| Frattini | C22 | C24×D173 |
| Fitting | C22×C42×C173 | C2 |
| socle | C24×C173 | C23 |
| prime radical | C24×D173 | C22 |
| cosocle | C22×C173 | C25 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
5632 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 17664);