Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | Aut(G) = C2×D3×D4×AGL(1,𝔽11) (order 10560) · Inn(G) = #63159 · Out(G) = C23×C5 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C11 ⋊ Q16 |
| Sylow | C11 ⋊ #216 |
| Sylow | C3 ⋊ #4326 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 528 |
Polycyclic presentation:
2^4,3,11|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^10,c^b=cd87 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#216, #11760958, D3×#4326, … |
| maximal normal subgroup of | D11×#216, #11760958, D3×#4326, … |
| maximal quotient of | #11760628, #11760631, #11760656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 77);