Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C23⋊#3866 |
| unambiguous semidirect product | C23⋊(C3×#3866) |
| Fitting, socle, Hall | C3×C23×C37 ⋊ C4 |
| derived, Hall | C23×C37 ⋊ C3×C4 |
| Hall | C3×C37 ⋊ Dic23 |
| Hall | C3×C23 ⋊ #3866 |
| Sylow | C37 ⋊ C3×Dic23 |
| Sylow | C23 ⋊ C3×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C23⋊#3866 |
| commutator, hypocenter | C23×C37 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C37 | C4 |
| prime radical | C3×C23×D37 | C2 |
| cosocle | C23×D37 | C2×C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
699 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 21);