Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | H(3,𝔽9)⋊C5 |
| Fitting, derived, Sylow | H(3,𝔽9) ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C32 | C34⋊C5 |
| commutator, Fitting, cosocle, hypocenter | H(3,𝔽9) | C5 |
| LCS | G ▷ H(3,𝔽9) | |
| UCS | C1 ◁ C32 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 405 |
Polycyclic presentation:
5,3^6|b^a=cd^2e^2g,c^a=b^2c^2ef^2g,d^a=b^2cd^2e^2f^2,e^a=b^2e,c^b=cf,d^b=dg,e^b=efg,d^c=df^2g,e^c=ef61 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 505);