Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #2158 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=df,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^662156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743536, #30743537, #30743541, … |
| maximal normal subgroup of | #30743536, #30743537, #30743541, … |
| maximal quotient of | #30767416, #30767480, #30767521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6294);