Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #536×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,h^b=h^66,e^c=eg755 conjugacy classes — view the full character table.
| maximal subgroup of | #30774845, #30774846, #30774852, … |
| maximal normal subgroup of | #30774845, #30774846, #30774852, … |
| maximal quotient of | #30828232, #30828263, #30828310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13888);