Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2186 |
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|c^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^c=h^66755 conjugacy classes — view the full character table.
| maximal subgroup of | #2186×D67, C2×#22562129, #31009604, … |
| maximal normal subgroup of | #2186×D67, C2×#22562129, #31009604, … |
| maximal quotient of | #30767936, #30768280, #30769040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6430);