Finite Group DatabasebetaFinite Group Databasebeta| order | 21543 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C167 · Schur multiplier (H2) = C1 |
| direct product | C43⋊C3×C167 |
| unambiguous semidirect product | C43⋊(C3×C167) |
| unambiguous semidirect product | (C43×C167)⋊C3 |
| Fitting, socle, Hall | C43×C167 ⋊ C3 |
| derived, Sylow | C43 ⋊ C3×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C3×C167 |
| Frattini | C1 | G |
| Fitting, socle | C43×C167 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C167 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7181 |
2839 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21543, 1);