Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C7 · Schur multiplier (H2) = C33 |
| direct product | C7×#10624854 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C7 | #6911 |
| commutator, Frattini | C3×C9 | C33×C7 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C7 ◁ C32×C7 ◁ C3×C7×3−1+2 ◁ G | |
178 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 414);