Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C13 |
| direct product | C47×#10621729 |
| Fitting, socle, Hall | C132×C47 ⋊ C4 |
| derived, Sylow | C132 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | #10621729 |
| commutator, hypocenter | C132 | C4×C47 |
| Frattini | C1 | G |
| Fitting, socle | C132×C47 | C4 |
| prime radical | C47×C13⋊D13 | C2 |
| cosocle | C13⋊D13 | C2×C47 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C47 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1222 |
2162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 28);