Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C271 · Schur multiplier (H2) = C27 |
| direct product | C2×#380×C271 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C271 | C23 |
| commutator | C22 | C23×C4×C271 |
| Frattini, cosocle | C23 | C24×C271 |
| prime radical | C25×C271 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C271 ◁ G | |
1232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
15176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 1010);