Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D33 |
| automorphism | Aut(G) = C23×D3×AGL(1,𝔽11) (order 5280) · Inn(G) = D33 · Out(G) = C24×C5 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D33 |
| Fitting | C3×C8×C11 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ D3×C8 |
| Sylow | C3 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D33 |
| commutator, hypocenter | C3×C11 | C2×C8 |
| Frattini | C4 | C2×D33 |
| Fitting | C3×C8×C11 | C2 |
| socle | C2×C3×C11 | C2×C4 |
| prime radical | C2×D33 | C4 |
| cosocle | C3×C4×C11 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | D33⋊C16, #11760473, C16×D33, … |
| maximal normal subgroup of | D33⋊C16, #11760473, C16×D33, … |
| maximal quotient of | C16×D33, #11760619, C8×Dic33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 63);