Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1778 |
220 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 117 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=de,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cg,h^a=h^66,d^b=dg,e^b=eg,h^c=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #30771128, #30771130, #30771132, … |
| maximal normal subgroup of | #30771128, #30771130, #30771132, … |
| maximal quotient of | #30747030, #30747031, #30747035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4418);