Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C24×C3×ΓL(1,𝔽8) |
| Fitting, socle | C24×C3×C7 ⋊ C3 |
| derived, Sylow | C7 ⋊ C24×C32 |
| Hall | C24×C7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C3 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C24×C32 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C7 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C24×C3 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 944);