Finite Group DatabasebetaFinite Group Databasebeta| order | 31724 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D7×D103 |
| unambiguous semidirect product | (D7×C103)⋊(C2×C11) |
| unambiguous semidirect product | (C7×D103)⋊(C2×C11) |
| unambiguous semidirect product | D721⋊(C2×C11) |
| Fitting, socle, Hall | C7×C11×C103 ⋊ C22 |
| derived, Hall | C7×C103 ⋊ C22×C11 |
| Hall | C11×C103 ⋊ C2×D7 |
| Sylow | C103 ⋊ C2×C11×D7 |
| Hall | C7×C11 ⋊ C2×D103 |
| Sylow | C7 ⋊ C2×C11×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D7×D103 |
| commutator, cosocle, hypocenter | C7×C103 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C103 | C22 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7931 |
2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31724, 11);