Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #510×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3416 |
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,h^b=h^66,d^c=dg,h^d=h^66560 conjugacy classes — view the full character table.
| maximal subgroup of | #31012581, #31012583, #31012590, … |
| maximal normal subgroup of | #31012581, #31012583, #31012590, … |
| maximal quotient of | #31008741, #31008749, #31008879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17655);