Finite Group Databasebeta

← Group #306636

Character table — Group #306636

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11-1-1111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-11111-1
χ91111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1111-1-111-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1-1-1-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111-1-11-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111-1-1-1111111-1-1-1
χ17222222222-22-22-22-22222-2-2000000-2-222000022000000-2-2000000000-2000000000
χ18222222222-22-22-22-22222-2-2000000-2-2-2-20000-2-2000000220000000002000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200000022220000-2-200000022000000000-2000000000
χ20222222222-22-22-22-2-2-2-2-2-2-200000022-2-2000022000000-2-20000000002000000000
χ2122222222-22-22-22-220000-2-22222220000-2-222000000-2-2000000-200000000000000
χ2222222222-22-22-22-220000-2-22222-2-2000022-2-2000000-2-2000000200000000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-2220000-2-2-2-200000022000000200000000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-2-2-20000222200000022000000-200000000000000
χ2522-22-2-2-222-2-222-2-220000-2200002-200002-200002i2i−2i−2i000000000002i−2i0000000000
χ2622-22-2-2-222-2-222-2-220000-2200002-200002-20000−2i−2i2i2i00000000000−2i2i0000000000
χ2722-22-2-2-222-2-222-2-220000-220000-220000-2200002i2i−2i−2i00000000000−2i2i0000000000
χ2822-22-2-2-222-2-222-2-220000-220000-220000-220000−2i−2i2i2i000000000002i−2i0000000000
χ2922-22-2-2-22-222-2-222-22i2i−2i−2i-220000002i−2i000000000000000000000000002i−2i00002-20
χ3022-22-2-2-22-222-2-222-22i2i−2i−2i-220000002i−2i00000000000000000000000000−2i2i0000-220
χ3122-22-2-2-22-222-2-222-2−2i−2i2i2i-22000000−2i2i000000000000000000000000002i−2i0000-220
χ3222-22-2-2-22-222-2-222-2−2i−2i2i2i-22000000−2i2i00000000000000000000000000−2i2i00002-20
χ3322-22-2-2-22-2-222-2-2222i2i−2i−2i2-200002-2−2i2i00-22000000000000000002i−2i000000000000
χ3422-22-2-2-22-2-222-2-2222i2i−2i−2i2-20000-22−2i2i002-200000000000000000−2i2i000000000000
χ3522-22-2-2-22-2-222-2-222−2i−2i2i2i2-200002-22i−2i00-2200000000000000000−2i2i000000000000
χ3622-22-2-2-22-2-222-2-222−2i−2i2i2i2-20000-222i−2i002-2000000000000000002i−2i000000000000
χ3722-2-222-2-2-20-2020202i−2i2i−2i0022−2−200002-200002i−2ii2−i2i2−i22−200i2i2−i2−i200000000002−2000
χ3822-2-222-2-2-20-2020202i−2i2i−2i0022−2−20000-220000−2i2ii2−i2i2−i22−200−i2−i2i2i20000000000−22000
χ3922-2-222-2-2-20-2020202i−2i2i−2i00−2−22200002-200002i−2i−i2i2−i2i2−2200−i2−i2i2i20000000000−22000
χ4022-2-222-2-2-20-2020202i−2i2i−2i00−2−2220000-220000−2i2i−i2i2−i2i2−2200i2i2−i2−i200000000002−2000
χ4122-2-222-2-2-20-202020−2i2i−2i2i0022−2−200002-20000−2i2i−i2i2−i2i22−200−i2−i2i2i200000000002−2000
χ4222-2-222-2-2-20-202020−2i2i−2i2i0022−2−20000-2200002i−2i−i2i2−i2i22−200i2i2−i2−i20000000000−22000
χ4322-2-222-2-2-20-202020−2i2i−2i2i00−2−22200002-20000−2i2ii2−i2i2−i2−2200i2i2−i2−i20000000000−22000
χ4422-2-222-2-2-20-202020−2i2i−2i2i00−2−2220000-2200002i−2ii2−i2i2−i2−2200−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-440-40-40404-4-44000000000000000000000000000000000000000000000
χ47444-4-4-44-440-40-4040-444-4000000000000000000000000000000000000000000000
χ48444-4-4-44-4-404040-40000000000000000000000022−22−222200000000000000000000000
χ49444-4-4-44-4-404040-400000000000000000000000−222222−2200000000000000000000000
χ5044-44-4-4-4444-4-444-4-400004-40000000000000000000000000000000000000000000
χ5144-4-444-4-44040-40-400000002222−22−220000000000000000−2222000000000000000000000
χ5244-4-444-4-44040-40-40000000−22−222222000000000000000022−22000000000000000000000
χ534-44-44-4-44040-40-4040000004i−4i4i−4i000000000000000000000000000000000000000
χ544-44-44-4-44040-40-404000000−4i4i−4i4i000000000000000000000000000000000000000
χ554-44-44-4-440-404040-40000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ564-44-44-4-440-404040-4000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ574-4-444-44-4000000000000002i2−2i2−2i22i20000000000000000002i2−2i22-2-22000000000000000
χ584-4-444-44-4000000000000002i2−2i2−2i22i2000000000000000000−2i22i2-222-2000000000000000
χ594-4-444-44-400000000000000−2i22i22i2−2i20000000000000000002i2−2i2-222-2000000000000000
χ604-4-444-44-400000000000000−2i22i22i2−2i2000000000000000000−2i22i22-2-22000000000000000
χ614-4-4-4-444404040-40-40000000000000000000000000000000000000000002i2−2i200000
χ624-4-4-4-444404040-40-4000000000000000000000000000000000000000000−2i22i200000
χ634-4-4-4-44440-40-404040000000000000000004-400000000000000000000000000000
χ644-4-4-4-44440-40-40404000000000000000000-4400000000000000000000000000000
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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