Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | #102×Dic67 |
| Sylow | C67 ⋊ C4×#102 |
396 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#102×D67, C2×#102×Dic67, C4×#16863389, … |
| maximal normal subgroup of | C4×#102×D67, C2×#102×Dic67, C4×#16863389, … |
| maximal quotient of | D4⋊C8×Dic67, #30746455, #30746470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4327);