Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C23⋊#3866) |
| unambiguous semidirect product | C23⋊(C3⋊#3866) |
| Fitting, socle, derived, Hall | C3×C23×C37 ⋊ C4 |
| Hall | C23×C37 ⋊ Dic3 |
| Hall | C3×C37 ⋊ Dic23 |
| Hall | C3×C23 ⋊ #3866 |
| Sylow | C37 ⋊ Dic69 |
| Sylow | C23 ⋊ C3⋊#3866 |
| Sylow | C3 ⋊ C23⋊#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C23×C37 | C4 |
| prime radical, cosocle | C3×C23×D37 | C2 |
| LCS | G ▷ C3×C23×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,23,37|a^2=b,c^a=c^2,d^a=d^22,e^a=e^31,e^b=e^36693 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 25);