Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #2177 |
172 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^66,d^b=df,f^b=fg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30776457, #30776459, #2177×D67, … |
| maximal normal subgroup of | #30776457, #30776459, #2177×D67, … |
| maximal quotient of | #30767582, #30767755, #30767839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6386);