Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1259712 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C33 |
| abelian | C32×C7×C81 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C27 | C33×C7 |
| socle | C33×C7 | C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
188 conjugacy classes of subgroups.
5103 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C32×C7×C81, C32×C7×C243, C3×C7×C9×C81, … |
| maximal normal subgroup of | C2×C32×C7×C81, C32×C7×C243, C3×C7×C9×C81, … |
| maximal quotient of | C2×C32×C7×C81, C32×C7×C243, C3×C7×C9×C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 391);