Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C73 · Schur multiplier (H2) = C214 |
| direct product | C22×#518×C73 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C73 | C24 |
| commutator | C2 | C25×C4×C73 |
| Frattini, cosocle | C22 | C26×C73 |
| prime radical | C24×D4×C73 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C73 ◁ G | |
14590 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
9928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 55633);