Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D47×D169 |
| unambiguous semidirect product | (C47×D169)⋊C2 |
| unambiguous semidirect product | (D47×C169)⋊C2 |
| unambiguous semidirect product | D7943⋊C2 |
| Fitting, derived, Hall | C47×C169 ⋊ C22 |
| Sylow | C169 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C47×C169 | C22 |
| Frattini | C13 | D13×D47 |
| socle | C13×C47 | C2×D13 |
| LCS | G ▷ C47×C169 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7943 |
2150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 8);