Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#11716875 |
| Fitting | C22×C52×D4 ⋊ C4 |
| Sylow | C52 ⋊ C22×#102 |
4288 conjugacy classes of subgroups; only the 486 normal subgroups are shown.
This group has 4288 conjugacy classes of subgroups — too many to draw. Only its 486 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D8×#1043, C22×#13104743, C2×#72220732, … |
| maximal normal subgroup of | C22×D8×#1043, C22×#13104743, C2×#72220732, … |
| maximal quotient of | C2×#72242325, C2×#72242326, C2×#72253151 |
Past the SmallGroups library coverage — no SmallGroups id.