Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C22×C13×SL(2,𝔽3) |
| Fitting, Hall | C22×Q8×C13 ⋊ C3 |
| derived | Q8 ⋊ C22×C3×C13 |
| Sylow | C22×Q8 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C13 | A4 |
| commutator, cosocle, hypocenter | Q8 | C22×C3×C13 |
| Frattini | C2 | C22×A4×C13 |
| Fitting | C22×Q8×C13 | C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C23×C13 | |
122 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, 1367);