Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #1889 |
578 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=df,b^a=bd,c^a=ce,e^a=eg,h^a=h^66,e^b=eg,h^b=h^66,d^c=dg,f^c=fg956 conjugacy classes — view the full character table.
| maximal subgroup of | #30771590, #30771592, #30771631, … |
| maximal normal subgroup of | #30771590, #30771592, #30771631, … |
| maximal quotient of | #30750517, #30750527, #30750801, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4919);