Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #418×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3138 |
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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=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,d^c=dg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30905593, #30905595, #30905597, … |
| maximal normal subgroup of | #30905593, #30905595, #30905597, … |
| maximal quotient of | #30856043, #30858553, #30858555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14882);