Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C8×C4⋊Dic67 |
| Sylow | C67 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742733, #30742734, #30742739, … |
| maximal normal subgroup of | #30742733, #30742734, #30742739, … |
| maximal quotient of | C8×C4⋊(C67⋊C8), #30746960, #30746975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4372);