Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#16863578 |
| Fitting | C2×C4⋊Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#456 |
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
956 conjugacy classes — view the full character table.
| maximal subgroup of | #30773176, #30773178, #30773186, … |
| maximal normal subgroup of | #30773176, #30773178, #30773186, … |
| maximal quotient of | C2×#22559170, C2×#22559204, C2×#22559177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13851);