Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C4×AGL(1,𝔽5)×SL(2,𝔽3) |
| unambiguous semidirect product | (C4×Q8×AGL(1,𝔽5))⋊C3 |
| Fitting | C4×C5×Q8 ⋊ C3×C4 |
| derived | C5×Q8 ⋊ C3×C42 |
| Hall | C4×Q8×AGL(1,𝔽5) ⋊ C3 |
| Sylow | C5 ⋊ C42×SL(2,𝔽3) |
458 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | SL(2,𝔽3)×GL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238226);