Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16863786 |
| Fitting | C2×#124×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#496 |
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #30750758, #30750760, #30757110, … |
| maximal normal subgroup of | #30750758, #30750760, #30757110, … |
| maximal quotient of | C2×#22559833, C2×#22559839, C2×#22559850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14945);