Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C9 |
| direct product | C9×#4294 |
| derived, Sylow | C19 ⋊ C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C19⋊C3 |
| commutator, hypocenter | C19 | C92 |
| Frattini | C32 | C3×C19⋊C3 |
| Fitting | C3×C9×C19 | C3 |
| socle, prime radical, cosocle | C32×C19 | C32 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C9 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | C27×#4294, #17987329, #17987330, … |
| maximal normal subgroup of | C27×#4294, #17987329, #17987330, … |
| maximal quotient of | #17987308, C27×#4294, C9×#10587018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 17);