Finite Group DatabasebetaFinite Group Databasebeta| order | 31668 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2 |
| direct product | C29×#10587716⋊C2 |
| unambiguous semidirect product | #10587716⋊(C2×C29) |
| unambiguous semidirect product | #10587720⋊(C2×C29) |
| unambiguous semidirect product | #10587722⋊(C2×C29) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #10587716⋊C2 |
| commutator, cosocle, hypocenter | C7×C13 | C22×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C29 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C29 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2639 |
696 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31668, 122);