Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1483 |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cfg,d^b=df,h^b=h^661358 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30747623, #30747625, #30747628, … |
| maximal normal subgroup of | #30747623, #30747625, #30747628, … |
| maximal quotient of | #30744263, #30744268, #30744273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2921);