Finite Group DatabasebetaFinite Group Databasebeta| order | 36771 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×(C103⋊C3)⋊C17 |
| unambiguous semidirect product | (C103⋊C3)⋊(C7×C17) |
| unambiguous semidirect product | (C103⋊C17)⋊(C3×C7) |
| unambiguous semidirect product | (C7×C103⋊C3)⋊C17 |
| Fitting, socle, Hall | C7×C103 ⋊ C3×C17 |
| derived, Sylow | C103 ⋊ C3×C7×C17 |
| Hall | C7×C103⋊C17 ⋊ C3 |
| Hall | C7×C103⋊C3 ⋊ C17 |
| Hall | C103⋊C17 ⋊ C3×C7 |
| Hall | C103⋊C3 ⋊ C7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C103⋊C3)⋊C17 |
| commutator, cosocle, hypocenter | C103 | C3×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C103 | C3×C17 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 721 |
371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36771, 7);