Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C9 · Schur multiplier (H2) = C33 |
| direct product | C5×#10624505 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C5 | #6866 |
| commutator | C33 | C3×C5×C9 |
| Frattini, cosocle | C34 | C32×C5 |
| prime radical | C32×C5×H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C5 ◁ C33×C5 ◁ C34×C5 ◁ G | |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 135 |
285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 65);