Finite Group DatabasebetaFinite Group Databasebeta| order | 31996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×D421 |
| unambiguous semidirect product | (D19×C421)⋊C2 |
| unambiguous semidirect product | (C19×D421)⋊C2 |
| unambiguous semidirect product | D7999⋊C2 |
| Fitting, socle, derived, Hall | C19×C421 ⋊ C22 |
| Sylow | C421 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D421 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C421 | C22 |
| LCS | G ▷ C19×C421 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7999 |
2332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31996, 8);