Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863660 |
| Fitting | C2×#108×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #30862691, C4×#16863660, #30862750, … |
| maximal normal subgroup of | #30862691, C4×#16863660, #30862750, … |
| maximal quotient of | C2×#22559551, C2×#22559585, C2×#22559647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14210);