Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16863207 |
| Fitting | C2×M32×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30771078, C4×#16863207, #30771123, … |
| maximal normal subgroup of | #30771078, C4×#16863207, #30771123, … |
| maximal quotient of | C2×#22558177, C2×#22558180, #30765603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6243);