Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#14523979 |
| Sylow | C67 ⋊ C22×#108 |
480 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 480 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.
2168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761715, #30761717, #30761720, … |
| maximal normal subgroup of | #30761715, #30761717, #30761720, … |
| maximal quotient of | C22×#16863147, C22×#16863149, C2×#22558957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13113);