Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,ℤ/8)×C13⋊C3 |
| unambiguous semidirect product | (C13×AGL(1,ℤ/8))⋊C3 |
| Fitting, Hall | C13×AGL(1,ℤ/8) ⋊ C3 |
| Sylow | C13 ⋊ C3×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2)(3,5)(4,6)(7,8)(10,11,13)(12,15,18)(14,17,16)(19,21,20);(2,5)(3,8)(6,7)(9,10,12,11,14,18,15,19,21,13,16,20,17);(2,6)(5,7)77 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×D13⋊C3, C13⋊C3×#453, #72229149, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D13⋊C3, C13⋊C3×#453, #72229149 |
| maximal quotient of | #72259483, C13⋊C3×#442 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 853);