Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊(C31⋊#64480) |
| unambiguous semidirect product | C31⋊(C3⋊#64480) |
| Fitting, socle | C3×C52×C31 ⋊ Dic3 |
| derived, Hall | C3×C31×C52⋊C3 ⋊ C4 |
| Hall | C52×C31 ⋊ C3⋊Dic3 |
| Hall | C3×C52⋊C3 ⋊ Dic31 |
| Sylow | C31 ⋊ C3⋊#64480 |
| Sylow | C52 ⋊ C3⋊Dic93 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C31×C52⋊C3 | C4 |
| Fitting, socle | C3×C52×C31 | Dic3 |
| prime radical, cosocle | C3×C31×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C3×C31×C52⋊C3 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,31,5^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^30,f^a=g^4,g^a=f,f^b=f^4,g^b=g^4,f^c=f^4g^2,g^c=f^2468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 531);