Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1377 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,d^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 | #30742580, #30742581, #30742592, … |
| maximal normal subgroup of | #30742580, #30742581, #30742592, … |
| maximal quotient of | #30742665, #30742675, #30742682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2594);