Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3385 |
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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=eg,b^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^66,f^c=fg953 conjugacy classes — view the full character table.
| maximal subgroup of | #30845328, #30845330, #30845373, … |
| maximal normal subgroup of | #30845328, #30845330, #30845373, … |
| maximal quotient of | #30872454, #30872487, #30874120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17418);