Finite Group DatabasebetaFinite Group Databasebeta| order | 20708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C167 · Schur multiplier (H2) = C1 |
| direct product | Dic31×C167 |
| unambiguous semidirect product | C31⋊(C4×C167) |
| derived, Sylow | C31 ⋊ C4×C167 |
| Hall | C31×C167 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C167 | D31 |
| commutator, hypocenter | C31 | C4×C167 |
| Frattini | C2 | D31×C167 |
| Fitting, socle, prime radical | C2×C31×C167 | C2 |
| cosocle | C2×C31 | C2×C167 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C167 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20708 |
5678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20708, 2);