Finite Group DatabasebetaFinite Group Databasebeta| order | 31724 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic1133 |
| unambiguous semidirect product | C11⋊(C7×Dic103) |
| unambiguous semidirect product | C103⋊(C7×Dic11) |
| derived, Hall | C11×C103 ⋊ C4×C7 |
| Hall | C7×C11×C103 ⋊ C4 |
| Hall | C7×C103 ⋊ Dic11 |
| Sylow | C103 ⋊ C7×Dic11 |
| Hall | C7×C11 ⋊ Dic103 |
| Sylow | C11 ⋊ C7×Dic103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D1133 |
| commutator, hypocenter | C11×C103 | C4×C7 |
| Frattini | C2 | C7×D1133 |
| Fitting, socle, prime radical | C2×C7×C11×C103 | C2 |
| cosocle | C2×C11×C103 | C2×C7 |
| LCS | G ▷ C11×C103 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31724 |
7952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31724, 4);