Finite Group DatabasebetaFinite Group Databasebeta| order | 5103 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C34 |
| direct product | ΓL(1,𝔽8)×#6900 |
| Fitting | C7×#6900 ⋊ C3 |
| Sylow | C7 ⋊ C3×#6900 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×ΓL(1,𝔽8) |
| commutator, socle | C32×C7 | C34 |
| Fitting | C7×#6900 | C3 |
| hypercenter | #6900 | ΓL(1,𝔽8) |
| hypocenter | C7 | C3×#6900 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6900 | |
1076 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1076 conjugacy classes of subgroups — too many to draw. Only its 355 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
255 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#92314, AGL(1,𝔽7)×#6900, #72229884, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#92314, AGL(1,𝔽7)×#6900, #72229884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5103, 3392);