Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of (C2×AGL(1,𝔽5))⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×(C2×AGL(1,𝔽5))⋊D5 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C5×D5) |
| Sylow | C53 ⋊ C22⋊C4 |
196 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #72229045, C5×AGL(1,𝔽5)×C22⋊D5, #72259439 |
| maximal normal subgroup of | #72229045, C5×AGL(1,𝔽5)×C22⋊D5, #72259439 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 635);