Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C35×C7 · Schur multiplier (H2) = C39 |
| direct product | C3×C7×H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C7 | C34 |
| commutator, Frattini | C3 | C35×C7 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C7 ◁ G | |
6776 conjugacy classes of subgroups.
1743 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 501);