Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊Dic11 |
| Hall | C3×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×D11 |
| commutator | C2×C3×C11 | C2×C4 |
| Fitting, socle, cosocle | C22×C3×C11 | C22 |
| prime radical | C22×D3×C11 | C2 |
| hypocenter | C3×C11 | C22⋊C4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C22 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|a^2=c,b^a=bd,f^a=f^10,e^b=e^278 conjugacy classes — view the full character table.
| maximal subgroup of | #11760739, #11760742, #11760744, … |
| maximal normal subgroup of | #11760739, #11760742, #11760744, … |
| maximal quotient of | (C2×D3)⋊(C11⋊C8), #11760496, #11760499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 25);