Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #3352 |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^66854 conjugacy classes — view the full character table.
| maximal subgroup of | #3352×D67, C2×#22572778, #31734585, … |
| maximal normal subgroup of | #3352×D67, C2×#22572778, #31734585, … |
| maximal quotient of | #30872233, #30872239, #30873609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17079);