Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C5×C9 · Schur multiplier (H2) = C35 |
| direct product | C5×#10624863 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C5 | C34 |
| commutator | C3 | C33×C5×C9 |
| Frattini, cosocle | C32 | C34×C5 |
| prime radical | C34×C5 | C32 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C5 ◁ G | |
944 conjugacy classes of subgroups.
| transitive degree | μt(G) = 405 |
1245 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 423);