Finite Group DatabasebetaFinite Group Databasebeta| order | 37386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D31⋊C9 |
| unambiguous semidirect product | D31⋊(C9×C67) |
| unambiguous semidirect product | (C31⋊C9)⋊(C2×C67) |
| derived, Sylow | C31 ⋊ C2×C9×C67 |
| Hall | C67×C31⋊C9 ⋊ C2 |
| Hall | D31×C67 ⋊ C9 |
| Hall | C31×C67 ⋊ C2×C9 |
| Hall | C31⋊C9 ⋊ C2×C67 |
| Hall | D31 ⋊ C9×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C67 | D31⋊C3 |
| commutator, hypocenter | C31 | C2×C9×C67 |
| Frattini | C3 | C67×D31⋊C3 |
| Fitting, socle | C3×C31×C67 | C2×C3 |
| prime radical | C3×D31×C67 | C3 |
| cosocle | C3×C31 | C2×C3×C67 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C67 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18693 |
2211 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37386, 18);