Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #427×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3059 |
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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,b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^66,d^c=dg,h^c=h^66956 conjugacy classes — view the full character table.
| maximal subgroup of | #30773284, #30773299, #30774570, … |
| maximal normal subgroup of | #30773284, #30773299, #30774570, … |
| maximal quotient of | #30838910, #30838949, #30838999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14166);