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 ⋊ #1521 |
218 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 77 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=fg,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^66,c^b=cf,d^b=dg,e^b=efg956 conjugacy classes — view the full character table.
| maximal subgroup of | #30748237, #30748238, #30748244, … |
| maximal normal subgroup of | #30748237, #30748238, #30748244, … |
| maximal quotient of | #30743853, #30743858, #30743873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3087);