Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #3139 |
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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,d^c=dg,h^c=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30753350, #30753371, #30753373, … |
| maximal normal subgroup of | #30753350, #30753371, #30753373, … |
| maximal quotient of | #30856045, #30858551, #30859513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14890);