Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C9 · Schur multiplier (H2) = C3 |
| direct product | C7×#10624453 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C7×C9 | H(3,𝔽3) |
| commutator | C33 | C3×C7×C9 |
| Frattini | C32×C9 | C32×C7 |
| socle | C32×C7 | C32⋊C9 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×C7×C9 ◁ C32×C7×C9 ◁ G | |
132 conjugacy classes of subgroups.
735 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 13);