Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C31⋊#11744620 |
| Fitting, derived, Hall | C32×C25×C31 ⋊ C4 |
| Hall | C25×C31 ⋊ #157 |
| Hall | C32×C31 ⋊ Dic25 |
| Hall | C32×C25 ⋊ Dic31 |
| Sylow | C31 ⋊ #11744620 |
| Sylow | C25 ⋊ C31⋊#157 |
| Sylow | C32 ⋊ Dic775 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C25×C31 | C4 |
| Frattini | C5 | C31⋊#4379 |
| socle | C32×C5×C31 | Dic5 |
| prime radical | C5×C3⋊D3×C31 | D5 |
| cosocle | C3⋊D3×C25×C31 | C2 |
| LCS | G ▷ C32×C25×C31 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,31,5|a^2=b,e^5=g^4,c^a=cd,d^a=cd^2,e^a=e^4g,f^a=f^30,g^a=g^4,c^b=c^2,d^b=d^22328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 201);