Finite Group DatabasebetaFinite Group Databasebeta| order | 34945 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C241⋊C5 |
| unambiguous semidirect product | C241⋊(C5×C29) |
| unambiguous semidirect product | (C29×C241)⋊C5 |
| Fitting, socle, Hall | C29×C241 ⋊ C5 |
| derived, Sylow | C241 ⋊ C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C241⋊C5 |
| commutator, cosocle, hypocenter | C241 | C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C241 | C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C29 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6989 |
1537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34945, 1);