Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C31⋊C9)⋊C25) |
| unambiguous semidirect product | (C31⋊C25)⋊(C22⋊C9) |
| unambiguous semidirect product | (C22⋊(C31⋊C9))⋊C25 |
| derived, Hall | C22×C31 ⋊ C9×C25 |
| Hall | C22×C31⋊C25 ⋊ C9 |
| Hall | C22⋊(C31⋊C9) ⋊ C25 |
| Hall | C31⋊C25 ⋊ C22⋊C9 |
| Sylow | C31 ⋊ C25×C22⋊C9 |
| Sylow | C22 ⋊ (C31⋊C9)⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C5 | C22⋊((C31⋊C3)⋊C5) |
| commutator, hypocenter | C22×C31 | C9×C25 |
| Fitting, socle, prime radical, cosocle | C22×C3×C5×C31 | C3×C5 |
| LCS | G ▷ C22×C31 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,2^2,31,3,5|a^3=f,b^5=g,c^a=d,d^a=cd,e^a=e^5,e^b=e^2420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 24);