Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D611 |
| unambiguous semidirect product | (C2×C13)⋊(C13×D47) |
| unambiguous semidirect product | (C2×C47)⋊(C13×D13) |
| Fitting, socle | C2×C132×C47 ⋊ C2 |
| derived | C13×C47 ⋊ C22×C13 |
| Hall | C132×C47 ⋊ C22 |
| Sylow | C132 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D611 |
| commutator, cosocle, hypocenter | C13×C47 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C47 | C2 |
| LCS | G ▷ C13×C47 | |
| UCS | C1 ◁ C2×C13 | |
64 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, 34);