Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic31⋊C9)⋊C25 |
| unambiguous semidirect product | (Dic31⋊C25)⋊C9 |
| unambiguous semidirect product | ((C31⋊C9)⋊C25)⋊C4 |
| derived, Sylow | C31 ⋊ C4×C9×C25 |
| Hall | (C31⋊C9)⋊C25 ⋊ C4 |
| Hall | Dic31⋊C25 ⋊ C9 |
| Hall | Dic31⋊C9 ⋊ C25 |
| Hall | C31⋊C25 ⋊ C4×C9 |
| Hall | C31⋊C9 ⋊ C4×C25 |
| Hall | Dic31 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3×C5 | AGL(1,𝔽31) |
| commutator, hypocenter | C31 | C4×C9×C25 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C31 | C2×C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3×C5 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,31,2,3,5|a^2=e,b^3=f,c^5=g,d^a=d^30,d^b=d^5,d^c=d^16930 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 2);