Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C8×C22⋊#1043 |
| Fitting | C22×C52×C8 ⋊ C4 |
| Sylow | C52 ⋊ C8×C22⋊C4 |
1536 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D4×#1043 |
| maximal normal subgroup of | C8×D4×#1043 |
| maximal quotient of | #72253173 |
Past the SmallGroups library coverage — no SmallGroups id.