Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #1376 |
148 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^a=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742584, #30742585, #30742586, … |
| maximal normal subgroup of | #30742584, #30742585, #30742586, … |
| maximal quotient of | #30742663, #30742675, #30742682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2592);