Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#21463203 |
| derived, Hall | C22×C13×C67 ⋊ C9 |
| Hall | C13×C67 ⋊ C22⋊C9 |
| Hall | C22×C67 ⋊ C13⋊C9 |
| Sylow | C67 ⋊ C22⋊(C13⋊C9) |
| Hall | C22×C13 ⋊ C67⋊C9 |
| Sylow | C13 ⋊ C22⋊(C67⋊C9) |
| Sylow | C22 ⋊ #21463203 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊#14579731 |
| commutator, hypocenter | C22×C13×C67 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C13×C67 | C3 |
| LCS | G ▷ C22×C13×C67 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15678 |
Polycyclic presentation:
3,2^2,13,67,3|a^3=f,b^a=c,c^a=bc,d^a=d^3,e^a=e^293492 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 61);