Finite Group DatabasebetaFinite Group Databasebeta| order | 31641 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C199⋊C3 |
| unambiguous semidirect product | C199⋊(C3×C53) |
| unambiguous semidirect product | (C53×C199)⋊C3 |
| Fitting, socle, Hall | C53×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C199⋊C3 |
| commutator, cosocle, hypocenter | C199 | C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10547 |
3657 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31641, 1);