Finite Group DatabasebetaFinite Group Databasebeta| order | 31524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37×C71 · Schur multiplier (H2) = C2 |
| direct product | A4×C37×C71 |
| unambiguous semidirect product | C22⋊(C3×C37×C71) |
| unambiguous semidirect product | (C22×C71)⋊(C3×C37) |
| Fitting, socle, Hall | C22×C37×C71 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C37×C71 |
| Hall | C22×C71 ⋊ C3×C37 |
| Hall | C22×C37 ⋊ C3×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37×C71 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C37×C71 |
| Frattini | C1 | G |
| Fitting, socle | C22×C37×C71 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C37×C71 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10508 |
10508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31524, 31);