Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C7×C9 · Schur multiplier (H2) = C35 |
| direct product | C3×C7×C9×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C7×C9 | C32 |
| commutator | C3 | C33×C7×C9 |
| Frattini | C32 | C34×C7 |
| socle | C33×C7 | C33 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C7×C9 ◁ G | |
1148 conjugacy classes of subgroups; only the 872 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 872 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2079 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 420);