Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C67⋊C9)⋊#261 |
| derived, Hall | C13×C67 ⋊ C4×C9 |
| Hall | C13×C67⋊C9 ⋊ C4 |
| Hall | C67⋊#261 ⋊ C9 |
| Hall | C67⋊C9 ⋊ #261 |
| Sylow | C67 ⋊ C9×#261 |
| Sylow | C13 ⋊ Dic67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C67⋊C3)⋊#261 |
| commutator, hypocenter | C13×C67 | C4×C9 |
| Fitting, socle | C3×C13×C67 | C3×C4 |
| prime radical, cosocle | C3×D13×C67 | C2×C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
Polycyclic presentation:
2,3,2,13,67,3|a^2=c,b^3=f,d^a=d^5,e^a=e^66,e^b=e^29,d^c=d^12327 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 35);