Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863163 |
| Sylow | C67 ⋊ C2×#342 |
680 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742950, #30742952, #342×Dic67, … |
| maximal normal subgroup of | #30742950, #30742952, #342×Dic67, … |
| maximal quotient of | C2×#22558052, #30745425, #30745431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4240);