Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3299 |
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^66,d^b=de,h^b=h^66,f^c=fg,h^d=h^66959 conjugacy classes — view the full character table.
| maximal subgroup of | #30845562, #30845570, #30845577, … |
| maximal normal subgroup of | #30845562, #30845570, #30845577, … |
| maximal quotient of | #103×D268, #30872073, #30873021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 16388);