Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊C8 |
| derived, Hall | C3×C11 ⋊ C2×C8 |
| Sylow | C11 ⋊ D3×C8 |
| Sylow | C3 ⋊ C8×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D11 |
| commutator, hypocenter | C3×C11 | C2×C8 |
| Fitting, cosocle | C3×C4×C11 | C22 |
| socle | C2×C3×C11 | C2×C4 |
| prime radical | C2×D33 | C4 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|a^2=c,b^2=c,c^2=d,f^a=f^10,e^b=e^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×D11, #11760696, #11760716, … |
| maximal normal subgroup of | D3×C8×D11, #11760696, #11760716, … |
| maximal quotient of | D33⋊C16, #11760473, #11760488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 7);