Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C47 · Schur multiplier (H2) = C1 |
| direct product | C13×C47×#261 |
| Fitting, socle, Hall | C132×C47 ⋊ C4 |
| derived | C13 ⋊ C4×C13×C47 |
| Sylow | C132 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C47 | #261 |
| commutator, hypocenter | C13 | C4×C13×C47 |
| Frattini | C1 | G |
| Fitting, socle | C132×C47 | C4 |
| prime radical | C13×D13×C47 | C2 |
| cosocle | D13 | C2×C13×C47 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C47 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2444 |
4277 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 20);