Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic2613 |
| unambiguous semidirect product | C67⋊(C3⋊Dic39) |
| derived, Hall | C32×C13×C67 ⋊ C4 |
| Hall | C13×C67 ⋊ C3⋊Dic3 |
| Hall | C32×C67 ⋊ Dic13 |
| Hall | C32×C13 ⋊ Dic67 |
| Sylow | C67 ⋊ C3⋊Dic39 |
| Sylow | C13 ⋊ C3⋊Dic201 |
| Sylow | C32 ⋊ Dic871 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D2613 |
| commutator, hypocenter | C32×C13×C67 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C13×C67 | C2 |
| LCS | G ▷ C32×C13×C67 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31356 |
Polycyclic presentation:
2,3^2,13,67,2|a^2=f,b^a=b^2,c^a=c^2,d^a=d^12,e^a=e^667842 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 114);