Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #87849 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×C22⋊#1042 |
| unambiguous semidirect product | C22⋊(C5×#1042) |
| Fitting | C22×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22⋊C4 |
260 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #72229001, C5×AGL(1,𝔽5)×C22⋊D5, #72259432 |
| maximal normal subgroup of | #72229001, C5×AGL(1,𝔽5)×C22⋊D5, #72259432 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 771);