Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #1508 |
294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 294 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,b^2=f,c^2=g,d^2=g,b^a=bd,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^b=h^661352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747432, #30747433, #30747437, … |
| maximal normal subgroup of | #30747432, #30747433, #30747437, … |
| maximal quotient of | #30743819, #30743828, #30743866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 3029);