Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C8×ΓL(1,𝔽8) |
| Fitting, Hall | C23×C7×C8 ⋊ C3 |
| derived, Sylow | C7 ⋊ C23×C3×C8 |
676 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(16,17,18)(19,21,20);(3,4)(15,16,17,19,18,20,21);(5,6);(7,8,9,10,11,12,13,14)320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10015);