Finite Group Databasebeta

← Group #312527

Character table — Group #312527

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-11-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111-11-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111111111-1-1-1
χ911111111111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ1011111111111111111-1-1-1-11111111-1-11111-1-111-1-1-1-111111111-1-11-1-1-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-111111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1111-1-1-111-1-11111-1
χ17222222222-22-22-22-2-20000-222222200-2-2-2-200000000-2-2000000002000000000000
χ18222222222-22-22-22-2-20000-22222-2-200222200000000-2-200000000-2000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-22200-2-222000000002200000000-2000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-20022-2-20000000022000000002000000000000
χ2122222222-22-22-22-22-22222-2000000-2-200002222000000-2-20000000-200000000000
χ2222222222-22-22-22-22-22222-2000000-2-20000-2-2-2-2000000220000000200000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200000022000022-2-2000000220000000-200000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000220000-2-222000000-2-20000000200000000000
χ2522-22-2-2-222-2-222-2-22-22i2i−2i−2i20000002i−2i000000000000000000000000002-22i−2i00000
χ2622-22-2-2-222-2-222-2-22-22i2i−2i−2i20000002i−2i00000000000000000000000000-22−2i2i00000
χ2722-22-2-2-222-2-222-2-22-2−2i−2i2i2i2000000−2i2i000000000000000000000000002-2−2i2i00000
χ2822-22-2-2-222-2-222-2-22-2−2i−2i2i2i2000000−2i2i00000000000000000000000000-222i−2i00000
χ2922-22-2-2-22-222-2-222-2-20000200002i−2i002i−2i0000002i2i−2i−2i0000000000002-2000000000
χ3022-22-2-2-22-222-2-222-2-20000200002i−2i002i−2i000000−2i−2i2i2i000000000000-22000000000
χ3122-22-2-2-22-222-2-222-2-2000020000−2i2i00−2i2i0000002i2i−2i−2i000000000000-22000000000
χ3222-22-2-2-22-222-2-222-2-2000020000−2i2i00−2i2i000000−2i−2i2i2i0000000000002-2000000000
χ3322-22-2-2-22-2-222-2-22222i2i−2i−2i-200002i−2i−2i2i−2i2i0000000000000000002-20000000000000
χ3422-22-2-2-22-2-222-2-22222i2i−2i−2i-20000−2i2i−2i2i2i−2i000000000000000000-220000000000000
χ3522-22-2-2-22-2-222-2-2222−2i−2i2i2i-200002i−2i2i−2i−2i2i000000000000000000-220000000000000
χ3622-22-2-2-22-2-222-2-2222−2i−2i2i2i-20000−2i2i2i−2i2i−2i0000000000000000002-20000000000000
χ372-22-22-2-22020-20-20202i−2i2i−2i0i2i2−i2−i2000000002-22i−2i2−22−2i2−i20022−2−20000000000i2−i2000
χ382-22-22-2-22020-20-20202i−2i2i−2i0i2i2−i2−i200000000-22−2i2i2−22−2i2−i200−2−2220000000000−i2i2000
χ392-22-22-2-22020-20-20202i−2i2i−2i0−i2−i2i2i2000000002-22i−2i−22−22−i2i200−2−2220000000000−i2i2000
χ402-22-22-2-22020-20-20202i−2i2i−2i0−i2−i2i2i200000000-22−2i2i−22−22−i2i20022−2−20000000000i2−i2000
χ412-22-22-2-22020-20-2020−2i2i−2i2i0i2i2−i2−i2000000002-2−2i2i−22−22i2−i200−2−2220000000000i2−i2000
χ422-22-22-2-22020-20-2020−2i2i−2i2i0i2i2−i2−i200000000-222i−2i−22−22i2−i20022−2−20000000000−i2i2000
χ432-22-22-2-22020-20-2020−2i2i−2i2i0−i2−i2i2i2000000002-2−2i2i2−22−2−i2i20022−2−20000000000−i2i2000
χ442-22-22-2-22020-20-2020−2i2i−2i2i0−i2−i2i2i200000000-222i−2i2−22−2−i2i200−2−2220000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-40000000000000022−2222−2200000000000000000022−222-22-2000000000000000
χ47444-4-44-4-40000000000000022−2222−22000000000000000000−2222-22-22000000000000000
χ48444-4-44-4-400000000000000−2222−222200000000000000000022−22-22-22000000000000000
χ49444-4-44-4-400000000000000−2222−2222000000000000000000−22222-22-2000000000000000
χ5044-44-4-4-4444-4-444-4-440000-40000000000000000000000000000000000000000000
χ514-444-4-44-44040-40-4000000000000000000000000000000022−22−2222000000000000000
χ524-444-4-44-44040-40-40000000000000000000000000000000−222222−22000000000000000
χ534-444-4-44-4-40-4040400000004i−4i−4i4i000000000000000000000000000000000000000
χ544-444-4-44-4-40-404040000000−4i4i4i−4i000000000000000000000000000000000000000
χ554-44-44-4-440-404040-40000002i22i2−2i2−2i20000000000000000−2i22i2000000000000000000000
χ564-44-44-4-440-404040-4000000−2i2−2i22i22i200000000000000002i2−2i2000000000000000000000
χ574-4-4444-4-440-40-404000000000000000004i−4i0000000000000000000000000000000
χ584-4-4444-4-440-40-40400000000000000000−4i4i0000000000000000000000000000000
χ594-4-4444-4-4-404040-4000000000000000000000000000000000000000000000002i2−2i20
χ604-4-4444-4-4-404040-400000000000000000000000000000000000000000000000−2i22i20
χ614-4-4-4-444404040-40-400000000000000000000002i2−2i2−2i22i200000000000000000000000
χ624-4-4-4-444404040-40-40000000000000000000000−2i22i22i2−2i200000000000000000000000
χ634-4-4-4-44440-40-4040404-4-4400000000000000000000000000000000000000000000
χ644-4-4-4-44440-40-404040-444-400000000000000000000000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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