Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1381 |
128 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 73 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=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^b=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #1381×D67, C2×#22558302, #30770719, … |
| maximal normal subgroup of | #1381×D67, C2×#22558302, #30770719, … |
| maximal quotient of | #30742700, #30742748, #30742750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2603);