Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×C22⋊D67 |
| Fitting | C22×SD16×C67 ⋊ C2 |
| Sylow | C67 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
959 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SD16×D67, C2×SD16×C22⋊D67, #31731120, … |
| maximal normal subgroup of | D4×SD16×D67, C2×SD16×C22⋊D67, #31731120, … |
| maximal quotient of | #30845294, #30845299, #30845309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16200);