Finite Group Databasebeta

← Group #145157

Character table — Group #145157

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order1222224444888888884444888888888888888888882244888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-11-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-11-11-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ9222222222222-2-222-2-2-2-2-2-222-2-20000000000000000020200-2-2000000000000
χ10222222222222-2-222-2-2-2-2-2-222-2-200000000000000000-20-20022000000000000
χ112222222222-2-222-2-222-2-2-2-2-2-22200000000000000002020-2-200000000000000
χ122222222222-2-222-2-222-2-2-2-2-2-2220000000000000000-20-202200000000000000
χ132222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000002-200
χ142222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000-2200
χ152222-2-22-22-200-2-200-2-200000022i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i220-200000i2i2−i2−i200000000
χ162222-2-22-22-200-2-200-2-200000022i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2-20200000−i2−i2i2i200000000
χ172222-2-22-22-200-2-200-2-200000022−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i220-200000−i2−i2i2i200000000
χ182222-2-22-22-200-2-200-2-200000022−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2-20200000i2i2−i2−i200000000
χ192222-2-2-22-22-2-200-2-20000002200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2020-200000000i2i2−i2−i20000
χ202222-2-2-22-22-2-200-2-20000002200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20-20200000000−i2−i2i2i20000
χ212222-2-2-22-22-2-200-2-20000002200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2020-200000000−i2−i2i2i20000
χ222222-2-2-22-22-2-200-2-20000002200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20-20200000000i2i2−i2−i20000
χ232-2-222-2-2-2222222-2-2-2-2-2-2222-22-200000000000000000000000000000000002i−2i
χ242-2-222-2-2-2222222-2-2-2-2-2-2222-22-20000000000000000000000000000000000−2i2i
χ252-2-222-2-2-22222-2-2-2-22222-2-22-2-220000000000000000000000002i−2i2i−2i00000000
χ262-2-222-2-2-22222-2-2-2-22222-2-22-2-22000000000000000000000000−2i2i−2i2i00000000
χ272-2-222-2-2-222-2-22222-2-222-2-2-222-200000000000000000000000000002i−2i2i−2i0000
χ282-2-222-2-2-222-2-22222-2-222-2-2-222-20000000000000000000000000000−2i2i−2i2i0000
χ292-2-222-2-2-222-2-2-2-22222-2-222-22-2222-2-222-2-222-2-222-2-200000000000000000000
χ302-2-222-2-2-222-2-2-2-22222-2-222-22-22-2-222-2-222-2-222-2-22200000000000000000000
χ312-2-22-222-2-222200-2-2000000-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000002i−2i00002−2−220000
χ322-2-22-222-2-222200-2-2000000-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000−2i2i0000−222−20000
χ332-2-22-222-2-222200-2-2000000-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000002i−2i0000−222−20000
χ342-2-22-222-2-222200-2-2000000-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000−2i2i00002−2−220000
χ352-2-22-22-222-2002200-2-2000000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i002−2−2200000000
χ362-2-22-22-222-2002200-2-2000000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i00−222−200000000
χ372-2-22-22-222-2002200-2-2000000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i00−222−200000000
χ382-2-22-22-222-2002200-2-2000000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i002−2−2200000000
χ39444444-4-4-4-400000000000000002222-2-2-2-2-2-2-2-2222200000000000000000000
χ40444444-4-4-4-40000000000000000-2-2-2-222222222-2-2-2-200000000000000000000
χ414444-4-44-44-400440044000000-4-4000000000000000000000000000000000000
χ424444-4-4-44-44440044000000-4-400000000000000000000000000000000000000
χ4344-4-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-200002−22−2ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ32−22−200000000000000000000
χ4444-4-40000002i2−2i22i2−2i22i2−2i22i2−2i22-22-20000−22−22−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−22−2200000000000000000000
χ4544-4-40000002i2−2i2−2i22i22i2−2i2−2i22i2-22-220000ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3−22−22−22−22ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ300000000000000000000
χ4644-4-40000002i2−2i2−2i22i22i2−2i2−2i22i2-22-220000−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ32−22−22−22−2−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ300000000000000000000
χ4744-4-4000000−2i22i22i2−2i2−2i22i22i2−2i2-22-220000ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3−22−22−22−22ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ300000000000000000000
χ4844-4-4000000−2i22i22i2−2i2−2i22i22i2−2i2-22-220000−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ32−22−22−22−2−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ300000000000000000000
χ4944-4-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-200002−22−2ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ32−22−200000000000000000000
χ5044-4-4000000−2i22i2−2i22i2−2i22i2−2i22i22-22-20000−22−22−ζ+2i+ζ3ζ−2i−ζ3−ζ+2i+ζ3ζ−2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−ζ−2i+ζ3ζ+2i−ζ3−22−2200000000000000000000
χ514-44-40000002i2−2i22i2−2i2−2i22i2−2i22i2-222-200002−2−22ζ−2i−ζ3−ζ+2i+ζ3−ζ+2i+ζ3ζ−2i−ζ3ζ+2i−ζ3−ζ−2i+ζ3−ζ−2i+ζ3ζ+2i−ζ32−2−2200000000000000000000
χ524-44-40000002i2−2i22i2−2i2−2i22i2−2i22i2-222-20000−222−2−ζ+2i+ζ3ζ−2i−ζ3ζ−2i−ζ3−ζ+2i+ζ3−ζ−2i+ζ3ζ+2i−ζ3ζ+2i−ζ3−ζ−2i+ζ3−222−200000000000000000000
χ534-44-40000002i2−2i2−2i22i2−2i22i22i2−2i22-2-220000ζ−2i−ζ3−ζ+2i+ζ3−ζ+2i+ζ3ζ−2i−ζ3−222−2−222−2ζ+2i−ζ3−ζ−2i+ζ3−ζ−2i+ζ3ζ+2i−ζ300000000000000000000
χ544-44-40000002i2−2i2−2i22i2−2i22i22i2−2i22-2-220000−ζ+2i+ζ3ζ−2i−ζ3ζ−2i−ζ3−ζ+2i+ζ32−2−222−2−22−ζ−2i+ζ3ζ+2i−ζ3ζ+2i−ζ3−ζ−2i+ζ300000000000000000000
χ554-44-4000000−2i22i22i2−2i22i2−2i2−2i22i22-2-220000ζ+2i−ζ3−ζ−2i+ζ3−ζ−2i+ζ3ζ+2i−ζ3−222−2−222−2ζ−2i−ζ3−ζ+2i+ζ3−ζ+2i+ζ3ζ−2i−ζ300000000000000000000
χ564-44-4000000−2i22i22i2−2i22i2−2i2−2i22i22-2-220000−ζ−2i+ζ3ζ+2i−ζ3ζ+2i−ζ3−ζ−2i+ζ32−2−222−2−22−ζ+2i+ζ3ζ−2i−ζ3ζ−2i−ζ3−ζ+2i+ζ300000000000000000000
χ574-44-4000000−2i22i2−2i22i22i2−2i22i2−2i2-222-200002−2−22ζ+2i−ζ3−ζ−2i+ζ3−ζ−2i+ζ3ζ+2i−ζ3ζ−2i−ζ3−ζ+2i+ζ3−ζ+2i+ζ3ζ−2i−ζ32−2−2200000000000000000000
χ584-44-4000000−2i22i2−2i22i22i2−2i22i2−2i2-222-20000−222−2−ζ−2i+ζ3ζ+2i−ζ3ζ+2i−ζ3−ζ−2i+ζ3−ζ+2i+ζ3ζ−2i−ζ3ζ−2i−ζ3−ζ+2i+ζ3−222−200000000000000000000
χ594-4-444-444-4-4000000000000000022-2-2-2-222-2-22222-2-200000000000000000000
χ604-4-444-444-4-40000000000000000-2-22222-2-222-2-2-2-22200000000000000000000
χ614-4-44-444-4-44-4-400440000004-400000000000000000000000000000000000000
χ624-4-44-44-444-400-4-400440000004-4000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.