Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#13104812 |
| Fitting | C25×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×#379 |
13856 conjugacy classes of subgroups; only the 678 normal subgroups are shown.
This group has 13856 conjugacy classes of subgroups — too many to draw. Only its 678 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
248 conjugacy classes — view the full character table.
| maximal subgroup of | #72223249, C2×#120×#1043, #72258310, … |
| maximal normal subgroup of | #72223249, C2×#120×#1043, #72258310, … |
| maximal quotient of | C2×#72221208 |
Past the SmallGroups library coverage — no SmallGroups id.