Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #3137 |
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 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=g,b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^66,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30925792, #30925796, #30925822, … |
| maximal normal subgroup of | #30925792, #30925796, #30925822, … |
| maximal quotient of | #30856039, #30858484, #30858493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14875);