Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1381 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^662156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743392, #30743393, #30743395, … |
| maximal normal subgroup of | #30743392, #30743393, #30743395, … |
| maximal quotient of | #30742701, #30742749, #30742874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2604);