Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D23×C37⋊C3 |
| unambiguous semidirect product | C23⋊(C22×C37⋊C3) |
| unambiguous semidirect product | (C2×C23)⋊(C2×C37⋊C3) |
| unambiguous semidirect product | (C2×C37×D23)⋊C3 |
| Fitting, socle | C2×C23×C37 ⋊ C2×C3 |
| derived, Hall | C23×C37 ⋊ C22×C3 |
| Hall | C2×C37×D23 ⋊ C3 |
| Hall | C23×C37⋊C3 ⋊ C22 |
| Sylow | C37 ⋊ C2×C3×D23 |
| Sylow | C23 ⋊ C22×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D23×C37⋊C3 |
| commutator, cosocle, hypocenter | C23×C37 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C37 | C2×C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
390 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D23×#66526, D3×D23×C37⋊C3, C2×C3×D23×C37⋊C3, … |
| maximal normal subgroup of | C2×D23×#66526, C2×C3×D23×C37⋊C3 |
| maximal quotient of | C2×D23×#66524, D3×D23×C37⋊C3, C2×C3×D23×C37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 19);