Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C31⋊#11744634 |
| derived, Hall | C31×C52⋊C9 ⋊ C4 |
| Hall | C52×C31 ⋊ Dic9 |
| Hall | C52⋊C9 ⋊ Dic31 |
| Sylow | C31 ⋊ #11744634 |
| Sylow | C52 ⋊ Dic279 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C31×C52⋊C9 | C4 |
| Frattini | C3 | C31⋊#64480 |
| Fitting, socle | C3×C52×C31 | Dic3 |
| prime radical | C3×C31×C5⋊D5 | D3 |
| cosocle | C31×(C5⋊D5)⋊C9 | C2 |
| LCS | G ▷ C31×C52⋊C9 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,31,5^2,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^30,e^a=e^3,f^a=ef^2,g^a=g^2,e^b=e^4,f^b=f^4,e^c=ef,f^c=e^2f^3468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 259);