Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #467×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3248 |
354 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^c=h^66,h^d=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #3248×D67, C2×#22571541, #31728657, … |
| maximal normal subgroup of | #3248×D67, C2×#22571541, #31728657, … |
| maximal quotient of | #30865731, #30865745, #30866218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15842);