Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,ℤ/8)×Dic67 |
| Sylow | C67 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #453×Dic67, #30861708, #454×Dic67, … |
| maximal normal subgroup of | #453×Dic67, #30861708, #454×Dic67, … |
| maximal quotient of | AGL(1,ℤ/8)×C67⋊C8, #30825416, #30825439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13320);