Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C9⋊(C31⋊#1039) |
| unambiguous semidirect product | C31⋊(C9⋊#1039) |
| derived, Hall | C52×C9×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ Dic9 |
| Hall | C9×C31 ⋊ #1039 |
| Hall | C52×C9 ⋊ Dic31 |
| Sylow | C31 ⋊ C9⋊#1039 |
| Sylow | C52 ⋊ Dic279 |
| Sylow | C9 ⋊ C31⋊#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊D1395 |
| commutator, hypocenter | C52×C9×C31 | C4 |
| Frattini | C2×C3 | C3⋊(C5⋊D155) |
| Fitting, cosocle | C2×C52×C9×C31 | C2 |
| socle, prime radical | C2×C3×C52×C31 | D3 |
| LCS | G ▷ C52×C9×C31 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,31,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^4,d^a=d^4,e^a=e^30,g^a=g^26978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 125);