Finite Group DatabasebetaFinite Group Databasebeta| order | 28561 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C133 · Schur multiplier (H2) = C134 |
| direct product | C13×H(3,𝔽13) |
| unambiguous semidirect product | C132⋊C132 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C132 | C132 |
| commutator, Frattini, cosocle | C13 | C133 |
| LCS | G ▷ C13 ▷ C1 | |
| UCS | C1 ◁ C132 ◁ G | |
| LECS | G ▷ C13 ▷ C1 | |
746 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2197 |
2353 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28561, 12);