Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C67 ⋊ #1426 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=cef,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^66,d^b=dg,h^b=h^66752 conjugacy classes — view the full character table.
| maximal subgroup of | #1426×D67, C2×#22558416, #30776350, … |
| maximal normal subgroup of | #1426×D67, C2×#22558416, #30776350, … |
| maximal quotient of | #30743513, #30743540, C2×#22558416 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2717);