Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#14523989 |
| Sylow | C67 ⋊ C22×Q32 |
360 conjugacy classes of subgroups.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #30772906, #30772907, #30772909, … |
| maximal normal subgroup of | #30772906, #30772907, #30772909, … |
| maximal quotient of | C22×#16863199, C22×#16863200, C22×#16863221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17622);