Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #1787 |
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^66,d^b=dg1358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747503, #30747504, #30747513, … |
| maximal normal subgroup of | #30747503, #30747504, #30747513, … |
| maximal quotient of | #30747202, #30747215, #30747276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4445);