Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Sylow | C7 ⋊ #10624877 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C32×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Frattini | C32 | C33×ΓL(1,𝔽8) |
| Fitting | C7×C9×H(3,𝔽3) | C3 |
| hypercenter | C9×H(3,𝔽3) | ΓL(1,𝔽8) |
| hypocenter | C7 | #10624877 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C3×C9 ◁ C9×H(3,𝔽3) | |
662 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
3^6,7|b^3=f,d^3=e,b^a=be,c^a=cf,g^b=g^2351 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 3382);