Finite Group DatabasebetaFinite Group Databasebeta| order | 34349 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C701⋊C7 |
| unambiguous semidirect product | C701⋊C72 |
| unambiguous semidirect product | (C7×C701)⋊C7 |
| Fitting, socle | C7×C701 ⋊ C7 |
| derived, Sylow | C701 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C701⋊C7 |
| commutator, cosocle, hypocenter | C701 | C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C701 | C7 |
| LCS | G ▷ C701 | |
| UCS | C1 ◁ C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4907 |
749 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34349, 3);