Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C67 ⋊ #2884 |
716 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^66,f^b=fg,d^c=dg1163 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30773423, #30773427, #30773437, … |
| maximal normal subgroup of | #30773423, #30773427, #30773437, … |
| maximal quotient of | #30821660, #30821664, #30821764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12974);