Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C2×C11×D12 |
| Fitting | C2×C3×C4×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ C2×D4 |
| Sylow | C3 ⋊ C2×D4×C11 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | #11760496, #11760503, #11760504, … |
| maximal normal subgroup of | #11760496, #11760503, #11760504, … |
| maximal quotient of | C11×#869, C4×C11×D12, C11×#874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 138);