Finite Group DatabasebetaFinite Group Databasebeta| order | 33666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D181⋊C3 |
| unambiguous semidirect product | D181⋊(C3×C31) |
| unambiguous semidirect product | (C181⋊C3)⋊(C2×C31) |
| Fitting, socle, Hall | C31×C181 ⋊ C2×C3 |
| derived, Sylow | C181 ⋊ C2×C3×C31 |
| Hall | C31×C181⋊C3 ⋊ C2 |
| Hall | C31×D181 ⋊ C3 |
| Hall | C181⋊C3 ⋊ C2×C31 |
| Hall | D181 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D181⋊C3 |
| commutator, cosocle, hypocenter | C181 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C181 | C2×C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5611 |
1116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33666, 13);