Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3103 |
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^c=h^66962 conjugacy classes — view the full character table.
| maximal subgroup of | #30750694, #30750700, #30751008, … |
| maximal normal subgroup of | #30750694, #30750700, #30751008, … |
| maximal quotient of | #30855839, #30858775, #30860677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14537);