Finite Group DatabasebetaFinite Group Databasebeta| order | 34010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3401 |
| unambiguous semidirect product | C19⋊(C5×D179) |
| unambiguous semidirect product | C179⋊(C5×D19) |
| Fitting, socle, Hall | C5×C19×C179 ⋊ C2 |
| derived, Hall | C19×C179 ⋊ C2×C5 |
| Hall | C5×C179 ⋊ D19 |
| Sylow | C179 ⋊ C5×D19 |
| Hall | C5×C19 ⋊ D179 |
| Sylow | C19 ⋊ C5×D179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3401 |
| commutator, cosocle, hypocenter | C19×C179 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C179 | C2 |
| LCS | G ▷ C19×C179 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17005 |
8510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34010, 4);