Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of Dic78 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#64625 |
| Fitting | C24×C3×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ C22×D4 |
| Sylow | C13 ⋊ C22×#67 |
| Sylow | C3 ⋊ C22×C22⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D39 |
| commutator, cosocle | C2×C3×C13 | C24 |
| Frattini | C2 | C23×D39 |
| Fitting | C24×C3×C13 | C2 |
| socle | C23×C3×C13 | C22 |
| hypercenter | C24 | D39 |
| hypocenter | C3×C13 | C22×D4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C23 ◁ C24 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1426);