Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×#1043 |
| Fitting | C52×H(5,𝔽2) ⋊ C4 |
| Sylow | C52 ⋊ C4×H(5,𝔽2) |
6640 conjugacy classes of subgroups; only the 1162 normal subgroups are shown.
This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 1162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
170 conjugacy classes — view the full character table.
| maximal subgroup of | C2×H(5,𝔽2)×#1043, #453×#1043, #72223366, … |
| maximal normal subgroup of | C2×H(5,𝔽2)×#1043, #453×#1043, #72223366, … |
| maximal quotient of | C2×H(5,𝔽2)×#1043, #535×#1043, #72223232, … |
Past the SmallGroups library coverage — no SmallGroups id.