Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1384 |
132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,d^b=dg,h^b=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #1384×D67, C2×#22558310, #30771115, … |
| maximal normal subgroup of | #1384×D67, C2×#22558310, #30771115, … |
| maximal quotient of | #30742706, #30742754, #30742756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2611);