Finite Group Databasebeta

← Group #305739

Character table — Group #305739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1-1111-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-11-1-11111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-111-1-11111-1-111-1
χ172222222222-2-22-22-2-22222-20000-2-20000002200-2-200002200000-20000000000000
χ182222222222-2-22-22-2-22222-20000-2-2000000-2-200220000-2-20000020000000000000
χ192222222222-2-22-22-2-2-2-2-2-2-20000220000002200220000-2-200000-20000000000000
χ202222222222-2-22-22-2-2-2-2-2-2-2000022000000-2-200-2-20000220000020000000000000
χ2122222222-2-222-22-22-20000-22222002222-2-200-2-2000000000000-200000000000000
χ2222222222-2-222-22-22-20000-2222200-2-2-2-22200-2-2000000000000200000000000000
χ2322222222-2-222-22-22-20000-2-2-2-2-20022-2-2-2-20022000000000000200000000000000
χ2422222222-2-222-22-22-20000-2-2-2-2-200-2-222220022000000000000-200000000000000
χ2522-22-2-22-22222-2-2-2-2222-2-2-200002-22-2002-20000000000000000002-200000000000
χ2622-22-2-22-22222-2-2-2-2222-2-2-200002-2-2200-22000000000000000000-2200000000000
χ2722-22-2-22-22222-2-2-2-22-2-222-20000-222-2002-2000000000000000000-2200000000000
χ2822-22-2-22-22222-2-2-2-22-2-222-20000-22-2200-220000000000000000002-200000000000
χ2922-22-2-22-222-2-2-22-22-222-2-220000-2200000000000000000000000000002i−2i002i−2i000
χ3022-22-2-22-222-2-2-22-22-222-2-220000-220000000000000000000000000000−2i2i00−2i2i000
χ3122-22-2-22-222-2-2-22-22-2-2-222200002-200000000000000000000000000002i−2i00−2i2i000
χ3222-22-2-22-222-2-2-22-22-2-2-222200002-20000000000000000000000000000−2i2i002i−2i000
χ3322-22-2-22-2-2-2222-22-2-2000020000002-200-220000002i2i−2i−2i00000000002i−2i000000000
χ3422-22-2-22-2-2-2222-22-2-2000020000002-200-22000000−2i−2i2i2i0000000000−2i2i000000000
χ3522-22-2-22-2-2-2222-22-2-200002000000-22002-20000002i2i−2i−2i0000000000−2i2i000000000
χ3622-22-2-22-2-2-2222-22-2-200002000000-22002-2000000−2i−2i2i2i00000000002i−2i000000000
χ372-2222-2-2-22-200-202002i−2i2i−2i022−2−2000000002i−2i2−200i2−i2i2−i22-222−2−200000000i2−i200000
χ382-2222-2-2-22-200-202002i−2i2i−2i022−2−200000000−2i2i2−200i2−i2i2−i2-22−2−22200000000−i2i200000
χ392-2222-2-2-22-200-202002i−2i2i−2i0−2−222000000002i−2i−2200−i2i2−i2i22-2−2−22200000000−i2i200000
χ402-2222-2-2-22-200-202002i−2i2i−2i0−2−22200000000−2i2i−2200−i2i2−i2i2-2222−2−200000000i2−i200000
χ412-2222-2-2-22-200-20200−2i2i−2i2i022−2−2000000002i−2i2−200−i2i2−i2i2-22−2−22200000000i2−i200000
χ422-2222-2-2-22-200-20200−2i2i−2i2i022−2−200000000−2i2i2−200−i2i2−i2i22-222−2−200000000−i2i200000
χ432-2222-2-2-22-200-20200−2i2i−2i2i0−2−222000000002i−2i−2200i2−i2i2−i2-2222−2−200000000−i2i200000
χ442-2222-2-2-22-200-20200−2i2i−2i2i0−2−22200000000−2i2i−2200i2−i2i2−i22-2−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ4644-44-4-44-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ4744-4-44-4-44000000000000002i2−2i22i2−2i20000000000002i2−2i20000002-22-2000000000000000
χ4844-4-44-4-44000000000000002i2−2i22i2−2i2000000000000−2i22i2000000-22-22000000000000000
χ4944-4-44-4-4400000000000000−2i22i2−2i22i20000000000002i2−2i2000000-22-22000000000000000
χ5044-4-44-4-4400000000000000−2i22i2−2i22i2000000000000−2i22i20000002-22-2000000000000000
χ514-4444-4-4-4-440040-400000002222−22−220000000000−2222000000000000000000000000000
χ524-4444-4-4-4-440040-40000000−22−222222000000000022−22000000000000000000000000000
χ534-44-4-4-444004-4040-400000000000000000000000000000000000000000000002i2−2i20
χ544-44-4-4-444004-4040-40000000000000000000000000000000000000000000000−2i22i20
χ554-44-4-4-44400-440-404000000000000004-4000000000000000000000000000000000
χ564-44-4-4-44400-440-40400000000000000-44000000000000000000000000000000000
χ574-4-44-44-444-40040-4004i−4i−4i4i00000000000000000000000000000000000000000000
χ584-4-44-44-444-40040-400−4i4i4i−4i00000000000000000000000000000000000000000000
χ594-4-44-44-44-4400-404000000000000000000000000022−22−2222000000000000000000000
χ604-4-44-44-44-4400-4040000000000000000000000000−222222−22000000000000000000000
χ614-4-4-4444-4004-40-40400000000000000000000000000000022−22−2222000000000000000
χ624-4-4-4444-4004-40-404000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4444-400-44040-40000004i−4i−4i4i000000000000000000000000000000000000000
χ644-4-4-4444-400-44040-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ65888-8-88-8-8000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).