Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #355×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1403 |
112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 112 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,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,d^b=deg,e^b=eg,f^b=fg,h^b=h^66,d^c=dfg,e^c=eg,e^d=eg446 conjugacy classes — view the full character table.
| maximal subgroup of | #1403×D67, C2×#22558356, #30776064, … |
| maximal normal subgroup of | #1403×D67, C2×#22558356, #30776064, … |
| maximal quotient of | #30743189, #30743256, #30743358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2657);