Finite Group DatabasebetaFinite Group Databasebeta| order | 31900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊#10596814 |
| unambiguous semidirect product | (C11⋊#10596814)⋊C5 |
| Fitting, socle, derived | C5×C11×C29 ⋊ C4×C5 |
| Hall | C5×C29×C11⋊C5 ⋊ C4 |
| Hall | C11×C29 ⋊ C5×AGL(1,𝔽5) |
| Hall | C5×C11⋊C5 ⋊ #1181 |
| Sylow | C29 ⋊ (C11⋊C5)⋊AGL(1,𝔽5) |
| Sylow | C11 ⋊ C5×#10596814 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C29 | C4×C5 |
| prime radical | C11⋊C5×D145 | C2 |
| cosocle | C11×D145 | C2×C5 |
| LCS | G ▷ C5×C11×C29 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1595 |
Polycyclic presentation:
2,5,2,5,11,29|a^2=c,d^a=d^2,e^a=e^10,f^a=f^17,e^b=e^4,d^c=d^4,f^c=f^28274 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31900, 72);