Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#102×D67 |
| Fitting | C2×#102×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#102 |
1072 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#102×D67, #1762×D67, #30853639, … |
| maximal normal subgroup of | C4×#102×D67, #1762×D67, #30853639, … |
| maximal quotient of | C2×D4⋊C8×D67, #1486×D67, C2×#22558632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12994);