Finite Group DatabasebetaFinite Group Databasebeta| order | 38591 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C37 · Schur multiplier (H2) = C1 |
| direct product | C7×C149⋊C37 |
| unambiguous semidirect product | C149⋊(C7×C37) |
| unambiguous semidirect product | (C7×C149)⋊C37 |
| Fitting, socle, Hall | C7×C149 ⋊ C37 |
| derived, Sylow | C149 ⋊ C7×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C149⋊C37 |
| commutator, cosocle, hypocenter | C149 | C7×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C149 | C37 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1043 |
287 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38591, 1);