Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1400 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^66,d^b=dg1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743173, #30743174, #30743175, … |
| maximal normal subgroup of | #30743173, #30743174, #30743175, … |
| maximal quotient of | #30743170, #30743230, #30743272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2650);