Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #368×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2161 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^c=h^66758 conjugacy classes — view the full character table.
| maximal subgroup of | #30776789, #30776792, #30776794, … |
| maximal normal subgroup of | #30776789, #30776792, #30776794, … |
| maximal quotient of | #30767417, #30767419, #30767481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6303);