Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #451×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3218 |
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|b^2=eg,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^66,c^b=ceg,h^b=h^66,f^c=fg653 conjugacy classes — view the full character table.
| maximal subgroup of | #30830109, #30830111, #30830123, … |
| maximal normal subgroup of | #30830109, #30830111, #30830123, … |
| maximal quotient of | #30865187, #30865565, #30866394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15540);