Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C11 ⋊ SD16 |
| Sylow | C11 ⋊ #215 |
| Sylow | C3 ⋊ #4314 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|a^2=d,b^2=c,c^2=d,b^a=bc,c^a=cd,f^a=f^10,e^b=e^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4314, #11760702, #11760713, … |
| maximal normal subgroup of | D3×#4314, #11760702, #11760713, … |
| maximal quotient of | #11760505, #11760508, #11760524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 17);