Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #323×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1468 |
280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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=e,e^2=g,b^a=bd,d^a=df,c^b=cg,e^b=ef,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #1468×D67, C2×#22558554, #30821788, … |
| maximal normal subgroup of | #1468×D67, C2×#22558554, #30821788, … |
| maximal quotient of | #30744160, #30744167, #30744180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2855);