Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1324 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^66,d^b=deg,d^c=dg950 conjugacy classes — view the full character table.
| maximal subgroup of | #30743209, #30743210, #30743211, … |
| maximal normal subgroup of | #30743209, #30743210, #30743211, … |
| maximal quotient of | #30742466, #30742473, #30742625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2454);