Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×D39 |
| Fitting | C22×C3×C4×C13 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C23×C4 |
| Sylow | C13 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C22×C4×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D39 |
| commutator, hypocenter | C3×C13 | C23×C4 |
| Frattini | C2 | C23×D39 |
| Fitting | C22×C3×C4×C13 | C2 |
| socle | C23×C3×C13 | C22 |
| prime radical | C23×D39 | C2 |
| cosocle | C2×C3×C13 | C24 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C22×C4 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1413);