Finite Group DatabasebetaFinite Group Databasebeta| order | 34030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | D5×C83⋊C41 |
| unambiguous semidirect product | C5⋊(C2×C83⋊C41) |
| unambiguous semidirect product | (D5×C83)⋊C41 |
| Fitting, socle, derived, Hall | C5×C83 ⋊ C2×C41 |
| Hall | C5×C83⋊C41 ⋊ C2 |
| Hall | D5×C83 ⋊ C41 |
| Sylow | C83 ⋊ D5×C41 |
| Sylow | C5 ⋊ C2×C83⋊C41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C83 | C2×C41 |
| LCS | G ▷ C5×C83 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 415 |
172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34030, 12);