Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| isoclinism | isoclinic class of C3⋊#3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C3⋊#3866 |
| unambiguous semidirect product | C3⋊(C23×#3866) |
| Fitting, socle, Hall | C3×C23×C37 ⋊ C4 |
| derived, Hall | C3×C37 ⋊ C4×C23 |
| Hall | C23×C37 ⋊ Dic3 |
| Hall | C3×C23 ⋊ #3866 |
| Sylow | C37 ⋊ Dic3×C23 |
| Sylow | C3 ⋊ C23×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊#3866 |
| commutator, hypocenter | C3×C37 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C37 | C4 |
| prime radical | C3×C23×D37 | C2 |
| cosocle | C3×D37 | C2×C23 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
759 conjugacy classes — view the full character table.
| maximal subgroup of | C23×C9⋊#3866, C23×C3⋊(#3866⋊C3), C3×C23×C3⋊#3866, … |
| maximal normal subgroup of | C23×C3⋊(#3866⋊C3), C3×C23×C3⋊#3866 |
| maximal quotient of | C23×C9⋊#3866, C3×C23×C3⋊#3866, C23×C3⋊(C3⋊#3866) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 23);