Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1 |
| direct product | C5×C31×C11⋊AGL(1,𝔽5) |
| Fitting, socle, Hall | C52×C11×C31 ⋊ C4 |
| derived | C5×C11 ⋊ C4×C5×C31 |
| Hall | C52×C31 ⋊ Dic11 |
| Hall | C11×C31 ⋊ C5×AGL(1,𝔽5) |
| Hall | C52×C11 ⋊ C4×C31 |
| Sylow | C52 ⋊ C31×Dic11 |
| Sylow | C11 ⋊ C5×AGL(1,𝔽5)×C31 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6820 |
3875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 275);