Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16863752 |
| Fitting | C2×#103×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#488 |
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 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.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #30863813, C4×#16863752, #30863824, … |
| maximal normal subgroup of | #30863813, C4×#16863752, #30863824, … |
| maximal quotient of | C2×#22560338, C2×#22560882, C2×#22560887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14827);