Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #413×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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=f,b^2=g,f^2=g,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^66,h^d=h^66767 conjugacy classes — view the full character table.
| maximal subgroup of | #30773387, #30773389, #30773391, … |
| maximal normal subgroup of | #30773387, #30773389, #30773391, … |
| maximal quotient of | #30821652, #30821654, #30821657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12991);