Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1763 |
324 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 129 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,b^2=f,c^2=eg,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^66,c^b=cg,h^b=h^661364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747721, #30747723, #30747735, … |
| maximal normal subgroup of | #30747721, #30747723, #30747735, … |
| maximal quotient of | #30746441, #30746451, #30746476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4343);