Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×(D13⋊C3)⋊C8 |
| unambiguous semidirect product | (D13⋊C3)⋊(C2×C8) |
| unambiguous semidirect product | (C2×D13⋊C8)⋊C3 |
| derived, Sylow | C13 ⋊ C22×C3×C8 |
| Hall | C2×D13⋊C8 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C22×C8 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C8×AGL(1,𝔽13), C2×#88100⋊C3, #72275914, … |
| maximal normal subgroup of | C2×C8×AGL(1,𝔽13), C2×#88100⋊C3, #72275914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1155);