Finite Group DatabasebetaFinite Group Databasebeta| order | 23421 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C211 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×C211 |
| unambiguous semidirect product | C37⋊(C3×C211) |
| Fitting, socle, Hall | C37×C211 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C211 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C3×C211 |
| Frattini | C1 | G |
| Fitting, socle | C37×C211 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C211 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7807 |
3165 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23421, 1);