Finite Group DatabasebetaFinite Group Databasebeta| order | 31900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D275⋊D29 |
| unambiguous semidirect product | D319⋊D25 |
| unambiguous semidirect product | D725⋊D11 |
| Fitting, derived, Hall | C11×C25×C29 ⋊ C22 |
| Hall | C25×C29 ⋊ C2×D11 |
| Hall | C11×C29 ⋊ C2×D25 |
| Hall | C11×C25 ⋊ C2×D29 |
| Sylow | C29 ⋊ D11×D25 |
| Sylow | C25 ⋊ D11×D29 |
| Sylow | C11 ⋊ D25×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C25×C29 | C22 |
| Frattini | C5 | D55⋊D29 |
| socle | C5×C11×C29 | C2×D5 |
| LCS | G ▷ C11×C25×C29 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7975 |
Polycyclic presentation:
2^2,5,11,29,5|c^5=f^4,d^a=d^10,e^a=e^28,c^b=c^4f,d^b=d^10,f^b=f^42044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31900, 39);