Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30627894⋊C2 |
| unambiguous semidirect product | #30627898⋊C2 |
| unambiguous semidirect product | #30627902⋊C2 |
| derived, Hall | C13×C67 ⋊ C22×C9 |
| Hall | #21463203 ⋊ C22 |
| Hall | D13×D67 ⋊ C9 |
| Sylow | C67 ⋊ C2×D13⋊C9 |
| Sylow | C13 ⋊ C2×D67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #19104944⋊C2 |
| commutator, hypocenter | C13×C67 | C22×C9 |
| Fitting, socle, cosocle | C3×C13×C67 | C22×C3 |
| prime radical | C3×D13×D67 | C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
Polycyclic presentation:
2^2,3,13,67,3|c^3=f,e^a=e^66,d^b=d^12,d^c=d^3,e^c=e^29312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 32);