Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16863518 |
| Sylow | C67 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
968 conjugacy classes — view the full character table.
| maximal subgroup of | #30771125, #30771127, #30771132, … |
| maximal normal subgroup of | #30771125, #30771127, #30771132, … |
| maximal quotient of | C2×SD16⋊(C67⋊C8), C2×#22559028, C2×#22559033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13406);