Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D33⋊Q8 |
| Hall | C3×C11 ⋊ C2×Q8 |
| Sylow | C11 ⋊ D3×Q8 |
| Sylow | C3 ⋊ Q8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D11 |
| commutator, socle, cosocle | C2×C3×C11 | C23 |
| Fitting | C3×C4×C11 | C22 |
| prime radical | C2×D33 | C22 |
| hypercenter | C4 | D3×D11 |
| hypocenter | C3×C11 | C2×Q8 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|a^2=d,b^2=d,c^2=d,c^a=cd,f^a=f^10,c^b=cd,e^b=e^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11760705, #11760714, #11760727, … |
| maximal normal subgroup of | #11760705, #11760714, #11760727, … |
| maximal quotient of | #11760732, #11760737, #11760740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 102);