Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1991 |
252 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 113 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=f,b^2=def,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^66,h^b=h^66968 conjugacy classes — view the full character table.
| maximal subgroup of | #30748381, #30748383, #1991×D67, … |
| maximal normal subgroup of | #30748381, #30748383, #1991×D67, … |
| maximal quotient of | #30755843, #30755859, #30755906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5476);