Finite Group DatabasebetaFinite Group Databasebeta| order | 34390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D181⋊C5 |
| unambiguous semidirect product | D181⋊(C5×C19) |
| unambiguous semidirect product | (C181⋊C5)⋊(C2×C19) |
| unambiguous semidirect product | (C19×D181)⋊C5 |
| Fitting, socle, Hall | C19×C181 ⋊ C2×C5 |
| derived, Sylow | C181 ⋊ C2×C5×C19 |
| Hall | C19×C181⋊C5 ⋊ C2 |
| Hall | C19×D181 ⋊ C5 |
| Hall | C181⋊C5 ⋊ C2×C19 |
| Hall | D181 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D181⋊C5 |
| commutator, cosocle, hypocenter | C181 | C2×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C181 | C2×C5 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3439 |
532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34390, 10);