Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(#3866⋊C3) |
| unambiguous semidirect product | (C23⋊#3866)⋊C3 |
| Fitting, socle, derived, Hall | C23×C37 ⋊ C3×C4 |
| Hall | C23⋊#3866 ⋊ C3 |
| Hall | C23×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ Dic23 |
| Sylow | C37 ⋊ C3×Dic23 |
| Sylow | C23 ⋊ #3866⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C37 | C3×C4 |
| prime radical | C23×D37⋊C3 | C2 |
| cosocle | C23×D37 | C2×C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,23,37|a^2=c,d^a=d^22,e^a=e^31,e^b=e^26,e^c=e^36147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 15);