Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C67 ⋊ #2241 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^662150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30769453, #30769454, #30769460, … |
| maximal normal subgroup of | #30769453, #30769454, #30769460, … |
| maximal quotient of | #30772211, #30773754, #30774049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6738);