Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3×AΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| Fitting, socle | C23×C3 ⋊ C2×ΓL(1,𝔽8) |
| derived | C3×AGL(1,𝔽8) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×AGL(1,𝔽8) | C2×C3 |
| Fitting, socle | C23×C3 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C3×AGL(1,𝔽8) | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 885);