Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3083 |
376 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^66,f^c=fg956 conjugacy classes — view the full character table.
| maximal subgroup of | #30913362, #30913365, #30913386, … |
| maximal normal subgroup of | #30913362, #30913365, #30913386, … |
| maximal quotient of | #30855356, #30856833, #30856866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 14359);