Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| isoclinism | isoclinic class of D3×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic3×Dic11 |
| derived, Hall | C3×C11 ⋊ C42 |
| Sylow | C11 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×D11 |
| commutator, hypocenter | C3×C11 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C3×C11 | C22 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×Dic22, #11760732, Dic6×Dic11, … |
| maximal normal subgroup of | Dic3×Dic22, #11760732, Dic6×Dic11, … |
| maximal quotient of | C3⋊C8×Dic11, Dic3×C11⋊C8, #11760488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 23);