Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C33×C9 |
| direct product | C3×#13133573 |
| Fitting | C3×C7×C92 ⋊ C3 |
| Sylow | C7 ⋊ C3×#6896 |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C32×ΓL(1,𝔽8) |
| commutator | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C3×C7×C92 | C3 |
| socle | C33×C7 | C33 |
| hypercenter | C3×C92 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6896 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C33 ◁ C3×C92 | |
884 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 364 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
639 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 3355);