Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1420 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^66,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^661346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1420×D67, C2×#22558403, #30776304, … |
| maximal normal subgroup of | #1420×D67, C2×#22558403, #30776304, … |
| maximal quotient of | #30743291, #30743396, #30743468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2704);