Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#135×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3067 |
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,f^c=fg,h^c=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30772786, #30772792, #30772842, … |
| maximal normal subgroup of | #30772786, #30772792, #30772842, … |
| maximal quotient of | #30838069, #30838097, #30838137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14226);