Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3185 |
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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=g,c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^c=dg,h^d=h^66560 conjugacy classes — view the full character table.
| maximal subgroup of | #30766681, #30766684, #31011066, … |
| maximal normal subgroup of | #30766681, #30766684, #31011066, … |
| maximal quotient of | #30856424, #30860156, #30860158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15250);