Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C22×C5×D3×D4 (order 960) · Inn(G) = D3 · Out(G) = C22×C5×D4 |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×C3⋊C8 |
| unambiguous semidirect product | (C2×C3)⋊(C8×C11) |
| derived, Sylow | C3 ⋊ C2×C8×C11 |
| Hall | C3×C11 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C11 | D3 |
| commutator, hypocenter | C3 | C2×C8×C11 |
| Frattini | C4 | C2×D3×C11 |
| Fitting | C2×C3×C4×C11 | C2 |
| socle, prime radical | C22×C3×C11 | C4 |
| cosocle | C3×C4 | C22×C11 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C4×C11 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊C8×Dic11, #11760488, #11760489, … |
| maximal normal subgroup of | C3⋊C8×Dic11, #11760488, #11760489, … |
| maximal quotient of | C4×C11×C3⋊C8, C11×C4⋊(C3⋊C8), C2×C11×C3⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 52);