Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14524067 |
| Fitting | C4×D8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
968 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14524067, #30825248, #30825262, … |
| maximal normal subgroup of | C8×#14524067, #30825248, #30825262, … |
| maximal quotient of | C8×#14524067, #30825409, #30825431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13313);