Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C24×C5×D3 (order 480) · Inn(G) = D3 · Out(G) = C24×C5 |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | D3×C8×C11 |
| Fitting | C3×C8×C11 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C8×C11 |
| Hall | C3×C11 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C11 | D3 |
| commutator, hypocenter | C3 | C2×C8×C11 |
| Frattini | C4 | C2×D3×C11 |
| Fitting | C3×C8×C11 | C2 |
| socle | C2×C3×C11 | C2×C4 |
| prime radical | C2×D3×C11 | C4 |
| cosocle | C3×C4 | C22×C11 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C8×C11 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 47);