Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D8×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C3×D8) |
| unambiguous semidirect product | (D8×D13)⋊C3 |
| Fitting | C13×D8 ⋊ C2×C3 |
| Hall | D8×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×D8 |
| Sylow | C13 ⋊ C2×C3×D8 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×D13⋊C3, D8×AGL(1,𝔽13), #72229208, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D13⋊C3, D8×AGL(1,𝔽13), #72229208, … |
| maximal quotient of | #72259450, C2×D8×D13⋊C3, #102×D13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 387);