Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D13⋊C3 |
| Fitting | C22×C4×C13 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C23×C3×C4 |
| Hall | C22×C4×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C23×C4 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#41×D13⋊C3, C4×D4×D13⋊C3, C22×C4×AGL(1,𝔽13), … |
| maximal normal subgroup of | C2×#41×D13⋊C3, C4×D4×D13⋊C3, C22×C4×AGL(1,𝔽13), … |
| maximal quotient of | C4×D4×D13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1243);