Finite Group DatabasebetaFinite Group Databasebeta| order | 35890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D185 |
| unambiguous semidirect product | C5⋊(D37×C97) |
| unambiguous semidirect product | C37⋊(D5×C97) |
| Fitting, socle, Hall | C5×C37×C97 ⋊ C2 |
| derived, Hall | C5×C37 ⋊ C2×C97 |
| Hall | C37×C97 ⋊ D5 |
| Hall | C5×C97 ⋊ D37 |
| Sylow | C37 ⋊ D5×C97 |
| Sylow | C5 ⋊ D37×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D185 |
| commutator, cosocle, hypocenter | C5×C37 | C2×C97 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C97 | C2 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C97 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17945 |
9118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35890, 7);