Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#16863216 |
| Sylow | C67 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30771148, C4×#16863216, #30771152, … |
| maximal normal subgroup of | #30771148, C4×#16863216, #30771152, … |
| maximal quotient of | C2×#22558272, #30767375, C2×#22558278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6272);