Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3168 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^662156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30765813, #30765816, #30765818, … |
| maximal normal subgroup of | #30765813, #30765816, #30765818, … |
| maximal quotient of | #30856378, #30860040, #30860050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15080);