Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of SL(2,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| direct product | C2×SL(2,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | SL(2,𝔽8) |
| commutator, hypocenter | SL(2,𝔽8) | C2 |
| Frattini | C1 | G |
| LCS | G ▷ SL(2,𝔽8) | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18 |
18 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 880);