Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C39 |
| direct product | C3×#13133542 |
| Fitting | C35×C7 ⋊ C3 |
| Sylow | C7 ⋊ C3×C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C32×ΓL(1,𝔽8) |
| commutator | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C35×C7 | C3 |
| socle | C33×C7 | C33 |
| hypercenter | C35 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C33 ◁ C35 | |
3824 conjugacy classes of subgroups.
639 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 3303);