Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×#41×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3005 |
758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^66,e^b=eg1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30887185, #30887190, #30887222, … |
| maximal normal subgroup of | #30887185, #30887190, #30887222, … |
| maximal quotient of | #30828216, #30828255, #30828294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13752);