Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2×C23 |
| Fitting, socle, Hall | C22×C5×C232 ⋊ C3 |
| derived, Hall | C22×C232 ⋊ C3×C5 |
| Hall | C5×C232 ⋊ A4 |
| Sylow | C232 ⋊ C5×A4 |
| Hall | C22×C5 ⋊ C232⋊C3 |
| Sylow | C22 ⋊ C5×C232⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C22⋊(C232⋊C3) |
| commutator, cosocle, hypocenter | C22×C232 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C232 | C3 |
| LCS | G ▷ C22×C232 | |
| UCS | C1 ◁ C5 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
3540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 102);