Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Hall | C32×C25×C41 ⋊ C4 |
| Hall | C25×C41 ⋊ #157 |
| Hall | C32×C41 ⋊ Dic25 |
| Hall | C32×C25 ⋊ #4223 |
| Sylow | C41 ⋊ #11744620 |
| Sylow | C25 ⋊ #13093287 |
| Sylow | C32 ⋊ #16861483 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C25×C41 | C4 |
| Frattini | C5 | #20301657 |
| socle | C32×C5×C41 | Dic5 |
| prime radical | C5×C3⋊D123 | D5 |
| cosocle | C25×C3⋊D123 | C2 |
| LCS | G ▷ C32×C25×C41 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6150 |
Polycyclic presentation:
2^2,3^2,5,41,5|a^2=b,e^5=g^4,c^a=cd,d^a=cd^2,e^a=e^4g,f^a=f^32,g^a=g^4,c^b=c^2,d^b=d^2,f^b=f^402328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 161);