Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D23×D37 |
| Fitting, socle, Hall | C3×C23×C37 ⋊ C22 |
| derived, Hall | C23×C37 ⋊ C22×C3 |
| Hall | C3×C37 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C3×D23 |
| Sylow | C23 ⋊ C2×C3×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D23×D37 |
| commutator, cosocle, hypocenter | C23×C37 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C37 | C22 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#66524⋊C2, C9×D23×D37, C3×D23×D37⋊C3, … |
| maximal normal subgroup of | D23×#66524⋊C2, C9×D23×D37, C3×D23×D37⋊C3, … |
| maximal quotient of | C9×D23×D37, C32×D23×D37, C3×D37×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 22);