Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22⋊C16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1315 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1315×D67, C2×#22558134, #30764901, … |
| maximal normal subgroup of | #1315×D67, C2×#22558134, #30764901, … |
| maximal quotient of | #30742457, #30742459, #30742461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2435);