Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C5 |
| direct product | #120×#1044 |
| Fitting | C52×#120 ⋊ C4 |
| Sylow | C52 ⋊ C4×#120 |
3110 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 3110 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
140 conjugacy classes — view the full character table.
| maximal subgroup of | #72221683, #1020×#1044, #120×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | #72221683, #120×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.