Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C7 · Schur multiplier (H2) = C36 |
| direct product | C7×#10624929 |
| subgroup | G/H | |
|---|---|---|
| center | C7×C9 | C3×H(3,𝔽3) |
| commutator, Frattini | C32 | C34×C7 |
| socle | C3×C7 | C32×H(3,𝔽3) |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C7×C9 ◁ C32×C7×C9 ◁ G | |
960 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 470 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
735 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 489);