Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1404 |
112 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 25 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,c^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^66,c^b=cg,d^b=de,e^b=eg,f^b=fg,d^c=dfg,e^c=eg,e^d=eg545 conjugacy classes — view the full character table.
| maximal subgroup of | #1404×D67, C2×#22558360, #30776080, … |
| maximal normal subgroup of | #1404×D67, C2×#22558360, #30776080, … |
| maximal quotient of | #30743193, #30743260, #30743356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2661);