Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C73 · Schur multiplier (H2) = C27×C4 |
| direct product | C73×#34178 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C25 |
| commutator | C22 | C24×C4×C73 |
| Frattini, cosocle | C23 | C25×C73 |
| prime radical | C25×C73 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ G | |
2806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 27166);