Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C67 ⋊ #1363 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=fg,d^2=ef,f^2=g,b^a=bc,c^a=ce,h^a=h^66,c^b=cf,d^b=def,f^b=fg,h^b=h^66953 conjugacy classes — view the full character table.
| maximal subgroup of | #1363×D67, C2×#22558262, #30767095, … |
| maximal normal subgroup of | #1363×D67, C2×#22558262, #30767095, … |
| maximal quotient of | #30742620, #30742623, #30743021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2563);