Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #346×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1333 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^66,c^b=ceg,d^b=dg,e^b=eg,h^b=h^661352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1333×D67, C2×#22558177, #30765596, … |
| maximal normal subgroup of | #1333×D67, C2×#22558177, #30765596, … |
| maximal quotient of | #30742487, #30742499, #30742599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2478);