Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C173 · Schur multiplier (H2) = C23×C4 |
| direct product | #2377×C173 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C173 | C24 |
| commutator | C22 | C23×C4×C173 |
| Frattini, cosocle | C23 | C24×C173 |
| prime radical | C2×#121×C173 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C173 ◁ G | |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
6574 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 1109);