Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×#4294 |
| derived, Sylow | C19 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C19⋊C3 |
| commutator, hypocenter | C19 | C32×C9 |
| Frattini | C3 | C32×C19⋊C3 |
| Fitting, socle, prime radical | C33×C19 | C3 |
| cosocle | C3×C19 | C33 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C33 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | #17987308, #17987336, #17987338, … |
| maximal normal subgroup of | #17987308, #17987336, #17987338, … |
| maximal quotient of | C3×C9×#4294, C3×C32⋊#4294, C3×#13095306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 39);