Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#16863532 |
| Fitting | C2×C22⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750967, #30750969, #30752277, … |
| maximal normal subgroup of | #30750967, #30750969, #30752277, … |
| maximal quotient of | C2×#22559129, C2×#22559197, C2×#22559146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13688);