Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C53 · Schur multiplier (H2) = C26×C4 |
| direct product | C53×#13776 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C53 | C24 |
| commutator | C22 | C22×C42×C53 |
| Frattini, cosocle | C24 | C24×C53 |
| prime radical | C25×C53 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
2318 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6784 |
4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6764);