Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1524 |
234 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 81 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=e,c^2=f,d^2=g,e^2=f,b^a=bd,d^a=df,h^a=h^66,d^b=dg,e^b=efg962 conjugacy classes — view the full character table.
| maximal subgroup of | #30746868, #30746871, #30746875, … |
| maximal normal subgroup of | #30746868, #30746871, #30746875, … |
| maximal quotient of | #30743770, #30743778, #30743790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3098);