Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | SL(2,𝔽3)×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C4⋊(AGL(1,𝔽5)×SL(2,𝔽3)) |
| unambiguous semidirect product | (Q8×C4⋊AGL(1,𝔽5))⋊C3 |
| Fitting | C4×C5×Q8 ⋊ C3×C4 |
| Hall | Q8×C4⋊AGL(1,𝔽5) ⋊ C3 |
| Sylow | C5 ⋊ C4⋊C4×SL(2,𝔽3) |
386 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238227);