Finite Group DatabasebetaFinite Group Databasebeta| order | 31712 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D991 |
| unambiguous semidirect product | C991⋊C25 |
| unambiguous semidirect product | (C2×C991)⋊C24 |
| Fitting, socle | C24×C991 ⋊ C2 |
| derived, Sylow | C991 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D991 |
| commutator, cosocle, hypocenter | C991 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C991 | C2 |
| LCS | G ▷ C991 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15856 |
7952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31712, 195);