Finite Group DatabasebetaFinite Group Databasebeta| order | 31284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C3 |
| direct product | C79×C3⋊Dic33 |
| unambiguous semidirect product | C3⋊(C79×Dic33) |
| unambiguous semidirect product | C11⋊(C3⋊Dic3×C79) |
| derived, Hall | C32×C11 ⋊ C4×C79 |
| Hall | C32×C11×C79 ⋊ C4 |
| Hall | C11×C79 ⋊ C3⋊Dic3 |
| Hall | C32×C79 ⋊ Dic11 |
| Sylow | C11 ⋊ C3⋊Dic3×C79 |
| Sylow | C32 ⋊ Dic11×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C79 | C3⋊D33 |
| commutator, hypocenter | C32×C11 | C4×C79 |
| Frattini | C2 | C79×C3⋊D33 |
| Fitting, socle, prime radical | C2×C32×C11×C79 | C2 |
| cosocle | C2×C32×C11 | C2×C79 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2×C79 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31284 |
8058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31284, 45);