Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊AGL(1,𝔽13) |
| unambiguous semidirect product | (D13⋊C3)⋊(C4⋊C4) |
| unambiguous semidirect product | (C2×C4⋊#261)⋊C3 |
| Fitting | C2×C4×C13 ⋊ C3×C4 |
| Hall | C2×C4⋊#261 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C4⋊C4 |
| Sylow | C13 ⋊ C2×C3×C4⋊C4 |
184 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×AGL(1,𝔽13), #72229007, #72229055, … |
| maximal normal subgroup of | C2×D4×AGL(1,𝔽13), #72229007, #72229055, … |
| maximal quotient of | #72229007, #72229085, #72229115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1159);