Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×D11 |
| Fitting | C3×Q8×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ C2×C3×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#215, D11×#216, #11760963, … |
| maximal normal subgroup of | D11×#215, D11×#216, #11760963, … |
| maximal quotient of | C3×#66940, C3×#66949, C3×#66941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 132);