Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #331×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1402 |
122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^66,d^b=deg,e^b=eg,f^b=fg,h^b=h^66,d^c=dfg,e^c=eg,e^d=eg644 conjugacy classes — view the full character table.
| maximal subgroup of | #1402×D67, C2×#22558355, #30776048, … |
| maximal normal subgroup of | #1402×D67, C2×#22558355, #30776048, … |
| maximal quotient of | #30743191, #30743258, #30743357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2656);