Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4×C5 |
| direct product | #127×#1044 |
| Fitting | C52×#127 ⋊ C4 |
| Sylow | C52 ⋊ C4×#127 |
2346 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 2346 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 | #72221577, #127×D5⋊AGL(1,𝔽5), #72258582 |
| maximal normal subgroup of | #72221577, #127×D5⋊AGL(1,𝔽5), #72258582 |
Past the SmallGroups library coverage — no SmallGroups id.