Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×#10624476 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C5 | #6856 |
| commutator, Frattini, cosocle | C34 | C32×C5 |
| prime radical | C34×C5 | C32 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C5 ◁ C33×C5 ◁ C34×C5 ◁ G | |
154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 135 |
205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 36);