Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863634 |
| Fitting | C22×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#467 |
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 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.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #30772776, #30772781, #30772832, … |
| maximal normal subgroup of | #30772776, #30772781, #30772832, … |
| maximal quotient of | C2×#22559571, C2×#22559605, C2×#22559657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14081);