Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×SL(2,𝔽3)×C25 |
| unambiguous semidirect product | (C2×Q8)⋊(C3×C25) |
| unambiguous semidirect product | (C2×Q8×C25)⋊C3 |
| Fitting, Hall | C2×Q8×C25 ⋊ C3 |
| derived | Q8 ⋊ C2×C3×C25 |
| Sylow | C2×Q8 ⋊ C3×C25 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 147);