Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C27 · Schur multiplier (H2) = C3 |
| direct product | C5×#10624503 |
| subgroup | G/H | |
|---|---|---|
| center | C5×C27 | H(3,𝔽3) |
| commutator | C32 | C3×C5×C27 |
| Frattini, cosocle | C3×C27 | C32×C5 |
| socle | C3×C5 | C32⋊C27 |
| prime radical | C5×H(3,𝔽3) | C27 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C5×C27 ◁ C3×C5×C27 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 248 |
| transitive degree | μt(G) = 1215 |
765 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 63);