Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1417 |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,c^2=ef,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=ce,e^b=ef,f^b=fg,h^b=h^662150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1417×D67, C2×#22558394, #30776284, … |
| maximal normal subgroup of | #1417×D67, C2×#22558394, #30776284, … |
| maximal quotient of | #30743282, #30743285, #30743393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2695);