Finite Group DatabasebetaFinite Group Databasebeta| order | 28561 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C13×C169 · Schur multiplier (H2) = C132 |
| unambiguous semidirect product | C132⋊C169 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, cosocle | C132 | C132 |
| commutator | C13 | C13×C169 |
| prime radical | C133 | C13 |
| LCS | G ▷ C13 ▷ C1 | |
| UCS | C1 ◁ C132 ◁ G | |
| LECS | G ▷ C132 ▷ C1 | |
83 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2197 |
Polycyclic presentation:
13^4|a^13=d,b^a=bc2353 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28561, 3);