Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #13093287⋊C25 |
| derived, Hall | C32×C41 ⋊ C4×C25 |
| Hall | C32×C41⋊C25 ⋊ C4 |
| Hall | #13093287 ⋊ C25 |
| Hall | C41⋊C25 ⋊ #157 |
| Sylow | C41 ⋊ C25×#157 |
| Sylow | C32 ⋊ #4223⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #13093287⋊C5 |
| commutator, hypocenter | C32×C41 | C4×C25 |
| Fitting, socle | C32×C5×C41 | C4×C5 |
| prime radical, cosocle | C5×C3⋊D123 | C2×C5 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6150 |
Polycyclic presentation:
2,5,2,3^2,41,5|a^2=c,b^5=g,d^a=de,e^a=de^2,f^a=f^32,f^b=f^10,d^c=d^2,e^c=e^2,f^c=f^40240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 102);