Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#20291879 |
| derived, Hall | C11×C31 ⋊ C4×C52 |
| Hall | C5×#13133724 ⋊ C4 |
| Hall | C31×Dic11 ⋊ C52 |
| Hall | Dic11 ⋊ C5×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×Dic11⋊C5 |
| Sylow | C11 ⋊ C4×C5×ΓL(1,𝔽32) |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6820 |
530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 94);