Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C73 · Schur multiplier (H2) = C213 |
| direct product | C22×#542×C73 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C73 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C73 |
| prime radical | C22×#121×C73 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C73 ◁ G | |
7974 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 55666);