Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C32 |
| direct product | C2×#72213866 |
| Sylow | C34 ⋊ C2×C4⋊Q8 |
1494 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
60 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72219722, #72220296, #72220305 |
| maximal normal subgroup of | C2×#72219722, #72220296, #72220305 |
Past the SmallGroups library coverage — no SmallGroups id.