Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×C5⋊GL(2,𝔽3) |
| Fitting | C2×C4×C5×Q8 ⋊ D3 |
| derived | C5×SL(2,𝔽3) ⋊ C22×C4 |
| Sylow | C5 ⋊ C2×C4×GL(2,𝔽3) |
766 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239423);