Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26 |
| direct product | AGL(1,ℤ/8)×C22⋊A4 |
| Fitting, Sylow | C24×AGL(1,ℤ/8) ⋊ C3 |
23736 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 23736 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,4,3)(6,8,7)(10,14)(13,16);(5,8)(6,7)(10,13)(11,15)(14,16);(1,4)(2,3)(9,10,11,13,12,14,15,16)88 conjugacy classes — view the full character table.
| maximal subgroup of | A42×AGL(1,ℤ/8), AGL(1,ℤ/8)×#1020 |
| maximal normal subgroup of | A42×AGL(1,ℤ/8), AGL(1,ℤ/8)×#1020 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,4,3)(6,8,7)(10,14)(13,16), (5,8)(6,7)(10,13)(11,15)(14,16), (1,4)(2,3)(9,10,11,13,12,14,15,16));