Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863513 |
| Sylow | C67 ⋊ C2×#443 |
472 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #30771068, #30771070, #30771075, … |
| maximal normal subgroup of | #30771068, #30771070, #30771075, … |
| maximal quotient of | C2×D8×C67⋊C8, C2×SD16×C67⋊C8, C2×Q16×C67⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13400);