Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3108 |
390 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,h^b=h^66,f^c=fg962 conjugacy classes — view the full character table.
| maximal subgroup of | #30825809, #30825813, #30825851, … |
| maximal normal subgroup of | #30825809, #30825813, #30825851, … |
| maximal quotient of | #30855848, #30858794, #30858795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14594);