Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×ΓL(1,𝔽32)⋊Dic11 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C5×Dic11) |
| derived, Hall | C11×C31 ⋊ C4×C52 |
| Hall | C5×C11×ΓL(1,𝔽32) ⋊ C4 |
| Hall | Dic341 ⋊ C52 |
| Hall | C5×ΓL(1,𝔽32) ⋊ Dic11 |
| Sylow | C31 ⋊ C52×Dic11 |
| Sylow | C11 ⋊ C5×Dic31⋊C5 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6820 |
680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 103);