Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C67 ⋊ #1369 |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,d^b=dg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #1369×D67, C2×#22558276, #30767394, … |
| maximal normal subgroup of | #1369×D67, C2×#22558276, #30767394, … |
| maximal quotient of | #30742568, #30742716, C2×#22558276 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2577);