Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C11 ⋊ Q16 |
| Sylow | C11 ⋊ #216 |
| Sylow | C3 ⋊ Dic44 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #63141 |
| commutator, Fitting, cosocle | C3×C4×C11 | C22 |
| Frattini, hypercenter | C4 | D3×D11 |
| socle, prime radical | C2×C3×C11 | D4 |
| hypocenter | C3×C11 | Q16 |
| LCS | G ▷ C3×C4×C11 ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ C4 | |
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=cd,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×Dic44, #11760713, #11760722, … |
| maximal normal subgroup of | D3×Dic44, #11760713, #11760722, … |
| maximal quotient of | #11760508, #11760511, #11760527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 21);