Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1838 |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cg,h^b=h^66,h^c=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30743243, #30750226, #30750227, … |
| maximal normal subgroup of | #30743243, #30750226, #30750227, … |
| maximal quotient of | #30749497, #30749499, #30749501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4650);