Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic611 |
| unambiguous semidirect product | C47⋊(C13×Dic13) |
| derived | C13×C47 ⋊ C4×C13 |
| Hall | C132×C47 ⋊ C4 |
| Sylow | C132 ⋊ Dic47 |
| Sylow | C47 ⋊ C13×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D611 |
| commutator, hypocenter | C13×C47 | C4×C13 |
| Frattini | C2 | C13×D611 |
| Fitting, socle, prime radical | C2×C132×C47 | C2 |
| cosocle | C2×C13×C47 | C2×C13 |
| LCS | G ▷ C13×C47 | |
| UCS | C1 ◁ C2×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2444 |
7982 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 15);