Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×AGL(1,𝔽8) |
| unambiguous semidirect product | C3⋊(C2×C3×AGL(1,𝔽8)) |
| unambiguous semidirect product | (C23×C3×D3)⋊C7 |
| Fitting, socle | C23×C32 ⋊ C2×C7 |
| derived | C23×C3 ⋊ C2×C3×C7 |
| Hall | C23×C3×D3 ⋊ C7 |
| Sylow | C32 ⋊ C2×AGL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×AGL(1,𝔽8) |
| commutator, cosocle, hypocenter | C23×C3 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32 | C2×C7 |
| LCS | G ▷ C23×C3 | |
| UCS | C1 ◁ C3 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 898);