Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C81 · Schur multiplier (H2) = C32 |
| direct product | C5×C32⋊C81 |
| unambiguous semidirect product | C32⋊(C5×C81) |
| unambiguous semidirect product | (C32×C5)⋊C81 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C5×C27 | C32 |
| commutator | C3 | C3×C5×C81 |
| Frattini, cosocle | C3×C27 | C32×C5 |
| socle | C32×C5 | C3×C27 |
| prime radical | C33×C5 | C27 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C5×C27 ◁ G | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1215 |
1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 61);