Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of SL(2,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| direct product | C3×SL(2,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3 | SL(2,𝔽8) |
| commutator, hypocenter | SL(2,𝔽8) | C3 |
| Frattini | C1 | G |
| LCS | G ▷ SL(2,𝔽8) | |
| UCS | C1 ◁ C3 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 27 |
27 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 780);