Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3165 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^66,d^c=dg758 conjugacy classes — view the full character table.
| maximal subgroup of | #30907936, #30907938, #30907940, … |
| maximal normal subgroup of | #30907936, #30907938, #30907940, … |
| maximal quotient of | #30856256, #30859217, #30859219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15054);