Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C7⋊PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×C7⋊PSU(3,𝔽2) |
| Fitting, socle, Hall | C33×C7 ⋊ Q8 |
| Sylow | C33 ⋊ Dic14 |
| Sylow | C7 ⋊ C3×PSU(3,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C7⋊PSU(3,𝔽2) |
| commutator, cosocle | C7×C3⋊D3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C33×C7 | Q8 |
| prime radical | C3×C7×C3⋊D3 | C22 |
| hypocenter | C32×C7 | C3×Q8 |
| LCS | G ▷ C7×C3⋊D3 ▷ C32×C7 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 830);