Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D39 |
| Fitting | C3×C42×C13 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C42 |
| Sylow | C13 ⋊ C42×D3 |
| Sylow | C3 ⋊ C42×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D39 |
| commutator, hypocenter | C3×C13 | C2×C42 |
| Frattini | C22 | C22×D39 |
| Fitting | C3×C42×C13 | C2 |
| socle, cosocle | C22×C3×C13 | C23 |
| prime radical | C22×D39 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C42 | |
216 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, 1045);