Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16863234 |
| Sylow | C67 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
764 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16863234, #30776413, #30776419, … |
| maximal normal subgroup of | C4×#16863234, #30776413, #30776419, … |
| maximal quotient of | C2×#22558387, C2×#22558389, C2×#22558410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6811);