Finite Group DatabasebetaFinite Group Databasebeta| order | 10252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D233 |
| unambiguous semidirect product | (D11×C233)⋊C2 |
| unambiguous semidirect product | (C11×D233)⋊C2 |
| unambiguous semidirect product | D2563⋊C2 |
| Fitting, socle, derived, Hall | C11×C233 ⋊ C22 |
| Sylow | C233 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D233 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C233 | C22 |
| LCS | G ▷ C11×C233 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
826 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×D233, D33×D233, D11×D699, … |
| maximal normal subgroup of | C3×D11×D233 |
| maximal quotient of | C3×D11×D233, D33×D233, D11×D699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10252, 8);