Finite Group DatabasebetaFinite Group Databasebeta| order | 34356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C409 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)⋊C4×C409 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C4×C409) |
| unambiguous semidirect product | Dic7⋊(C3×C409) |
| derived, Sylow | C7 ⋊ C3×C4×C409 |
| Hall | Dic7×C409 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C409 ⋊ C4 |
| Hall | C7×C409 ⋊ C3×C4 |
| Hall | Dic7 ⋊ C3×C409 |
| Hall | ΓL(1,𝔽8) ⋊ C4×C409 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11452 |
5726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34356, 18);