Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D39 |
| Fitting, socle | C24×C3×C13 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C25 |
| Sylow | C13 ⋊ C24×D3 |
| Sylow | C3 ⋊ C24×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C13 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C24 | |
1496 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, 1459);