Finite Group DatabasebetaFinite Group Databasebeta| order | 31900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| derived, Hall | C11×C29 ⋊ C22×C25 |
| Hall | C29×C11⋊C25 ⋊ C22 |
| Hall | D11×D29 ⋊ C25 |
| Hall | C11⋊C25 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D11⋊C25 |
| Sylow | C11 ⋊ C2×C25×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D29×AGL(1,𝔽11) |
| commutator, hypocenter | C11×C29 | C22×C25 |
| Fitting, socle, cosocle | C5×C11×C29 | C22×C5 |
| prime radical | C5×D11×D29 | C5 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7975 |
880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31900, 15);