Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#131⋊C3 |
| unambiguous semidirect product | #131⋊(C3×C13) |
| Fitting, Hall | C13×#131 ⋊ C3 |
| Sylow | #131 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C13 | A4 |
| commutator, hypocenter | Q8 | C3×C4×C13 |
| Frattini | C4 | C2×A4×C13 |
| Fitting | C13×#131 | C3 |
| socle | C2×C13 | C4×A4 |
| prime radical | C13×#41⋊C3 | C2 |
| cosocle | #41 | C2×C3×C13 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C8×C13 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 861);