Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C13⋊D611 |
| unambiguous semidirect product | (C2×C13)⋊D611 |
| unambiguous semidirect product | (C2×C47)⋊(C13⋊D13) |
| Fitting, socle | C2×C132×C47 ⋊ C2 |
| derived, Hall | C132×C47 ⋊ C22 |
| Sylow | C132 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊D611 |
| commutator, cosocle, hypocenter | C132×C47 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C47 | C2 |
| LCS | G ▷ C132×C47 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15886 |
7946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 36);