Finite Group DatabasebetaFinite Group Databasebeta| order | 34364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D71×D121 |
| unambiguous semidirect product | (C71×D121)⋊C2 |
| unambiguous semidirect product | (C121×D71)⋊C2 |
| unambiguous semidirect product | D8591⋊C2 |
| Fitting, derived, Hall | C71×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D71 |
| Sylow | C71 ⋊ C2×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C71×C121 | C22 |
| Frattini | C11 | D11×D71 |
| socle | C11×C71 | C2×D11 |
| LCS | G ▷ C71×C121 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8591 |
2294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34364, 6);