Finite Group DatabasebetaFinite Group Databasebeta| order | 39402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#13184226⋊C2 |
| Fitting, socle, Hall | C11×C199 ⋊ C2×C9 |
| derived, Sylow | C199 ⋊ C2×C9×C11 |
| Hall | C11×#13184226 ⋊ C2 |
| Hall | C11×D199 ⋊ C9 |
| Hall | #13184226 ⋊ C2×C11 |
| Hall | D199 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #13184226⋊C2 |
| commutator, hypocenter | C199 | C2×C9×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C199 | C2×C9 |
| prime radical | C11×D199⋊C3 | C3 |
| cosocle | C199⋊C3 | C2×C3×C11 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(39402, 31);