Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#14523962 |
| Sylow | C67 ⋊ C22×#101 |
736 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761153, #30761154, #30761198, … |
| maximal normal subgroup of | #30761153, #30761154, #30761198, … |
| maximal quotient of | C22×#16863122, C2×#22558533, C2×#22558539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12980);