Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #2057 |
282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 99 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=d,b^2=d,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^66,c^b=cf,e^c=eg,h^c=h^661352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30744624, #30744625, #30744630, … |
| maximal normal subgroup of | #30744624, #30744625, #30744630, … |
| maximal quotient of | #30760235, #30760245, #30760269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 5839);