Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C42×D5⋊AGL(1,𝔽5) |
| Fitting | C42×C52 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C2×C43 |
2802 conjugacy classes of subgroups; only the 759 normal subgroups are shown.
This group has 2802 conjugacy classes of subgroups — too many to draw. Only its 759 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72221577, #72221613, #127×D5⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #72221577, #72221613, #127×D5⋊AGL(1,𝔽5), … |
| maximal quotient of | C2×C42×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.