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 ⋊ #4324 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|a^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^10,c^b=cd,e^b=e^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11760705, #11760706, #11760729, … |
| maximal normal subgroup of | #11760705, #11760706, #11760729, … |
| maximal quotient of | #11760503, #11760507, #11760523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 15);