Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×#41×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3002 |
764 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^66,e^b=eg1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30750937, #30750943, #30827933, … |
| maximal normal subgroup of | #30750937, #30750943, #30827933, … |
| maximal quotient of | #30827937, #30827988, #30828039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13728);