Finite Group DatabasebetaFinite Group Databasebeta| order | 10252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#11745400 |
| Fitting, socle, Hall | C11×C233 ⋊ C4 |
| derived, Sylow | C233 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #11745400 |
| commutator, hypocenter | C233 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C233 | C4 |
| prime radical | C11×D233 | C2 |
| cosocle | D233 | C2×C11 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
682 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11×#11745400, C11×C3⋊#11745400 |
| maximal normal subgroup of | C3×C11×#11745400 |
| maximal quotient of | C3×C11×#11745400, C11×C3⋊#11745400 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10252, 6);