Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C173 · Schur multiplier (H2) = C29 |
| direct product | C2×#520×C173 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C173 | C24 |
| commutator | C2 | C24×C4×C173 |
| Frattini, cosocle | C22 | C25×C173 |
| prime radical | C22×#41×C173 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C173 ◁ G | |
1640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
11764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 2159);