Finite Group Databasebeta

← Group #305741

Character table — Group #305741

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-111111111111111-1-1-11-1-1-1-1-1-1-1-111-1
χ311111111111111111111111111-1-11111111111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-111-1-111-1
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ111111111111111111-1-1-1-1111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-111111-1-1-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-1-111-1-11111-1
χ172222222222-2-2-222-22222-2-20000220000-2-2000022-2-200000000000-200000000000
χ182222222222-2-2-222-22222-2-20000-2-20000-2-20000-2-22200000000000200000000000
χ192222222222-2-2-222-2-2-2-2-2-2-20000220000220000-2-22200000000000-200000000000
χ202222222222-2-2-222-2-2-2-2-2-2-20000-2-2000022000022-2-200000000000200000000000
χ2122222222-2-2222-2-220000-2-222220022-2-200-2-2-2-2000000000000200000000000000
χ2222222222-2-2222-2-220000-2-2222200-2-2220022-2-2000000000000-200000000000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-200222200-2-222000000000000-200000000000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-200-2-2-2-2002222000000000000200000000000000
χ2522-22-2-2-222222-2-2-2-222-2-22-20000002-2002-22-2000000000000000000002-20000000
χ2622-22-2-2-222222-2-2-2-222-2-22-2000000-22002-2-2200000000000000000000-220000000
χ2722-22-2-2-222222-2-2-2-2-2-2222-20000002-200-222-200000000000000000000-220000000
χ2822-22-2-2-222222-2-2-2-2-2-2222-2000000-2200-22-22000000000000000000002-20000000
χ2922-22-2-2-2222-2-22-2-2222-2-2-220000000000-22000000000000000002i−2i000002i−2i00000
χ3022-22-2-2-2222-2-22-2-2222-2-2-220000000000-2200000000000000000−2i2i00000−2i2i00000
χ3122-22-2-2-2222-2-22-2-22-2-222-2200000000002-2000000000000000002i−2i00000−2i2i00000
χ3222-22-2-2-2222-2-22-2-22-2-222-2200000000002-200000000000000000−2i2i000002i−2i00000
χ3322-22-2-2-22-2-222-222-20000-220000002-20000-220000002i2i−2i−2i000000002i−2i000000000
χ3422-22-2-2-22-2-222-222-20000-220000002-20000-22000000−2i−2i2i2i00000000−2i2i000000000
χ3522-22-2-2-22-2-222-222-20000-22000000-2200002-20000002i2i−2i−2i00000000−2i2i000000000
χ3622-22-2-2-22-2-222-222-20000-22000000-2200002-2000000−2i−2i2i2i000000002i−2i000000000
χ3722-2-2-222-22-20002-202-22-200i2i2−i2−i22i−2i00000000i2−i22i−2i00i2−i2i2−i222−2−20000000000002−20
χ3822-2-2-222-22-20002-202-22-200i2i2−i2−i2−2i2i00000000i2−i2−2i2i00i2−i2i2−i2−2−222000000000000−220
χ3922-2-2-222-22-20002-202-22-200−i2−i2i2i22i−2i00000000−i2i22i−2i00−i2i2−i2i2−2−222000000000000−220
χ4022-2-2-222-22-20002-202-22-200−i2−i2i2i2−2i2i00000000−i2i2−2i2i00−i2i2−i2i222−2−20000000000002−20
χ4122-2-2-222-22-20002-20-22-2200i2i2−i2−i22i−2i00000000i2−i2−2i2i00−i2i2−i2i2−2−2220000000000002−20
χ4222-2-2-222-22-20002-20-22-2200i2i2−i2−i2−2i2i00000000i2−i22i−2i00−i2i2−i2i222−2−2000000000000−220
χ4322-2-2-222-22-20002-20-22-2200−i2−i2i2i22i−2i00000000−i2i2−2i2i00i2−i2i2−i222−2−2000000000000−220
χ4422-2-2-222-22-20002-20-22-2200−i2−i2i2i2−2i2i00000000−i2i22i−2i00i2−i2i2−i2−2−2220000000000002−20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-44-4000-4404-4-44000000000000000000000000000000000000000000000
χ47444-44-4-4-44-4000-440-444-4000000000000000000000000000000000000000000000
χ48444-44-4-4-4-440004-400000000000000000000000000022−22−22220000000000000000000
χ49444-44-4-4-4-440004-4000000000000000000000000000−222222−220000000000000000000
χ5044-44-4-4-44-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ5144-4-4-444-4-44000-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5244-4-4-444-4-44000-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ534-44-4-4-444004-4400-40000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ544-44-4-4-444004-4400-4000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ554-44-4-4-44400-44-40040000004-44-4000000000000000000000000000000000000000
χ564-44-4-4-44400-44-4004000000-44-44000000000000000000000000000000000000000
χ574-4-444-44-4000000000000002i2−2i2−2i22i20000000000000022−2200002i−2i−2i2i000000000000000
χ584-4-444-44-4000000000000002i2−2i2−2i22i200000000000000−22220000−2i2i2i−2i000000000000000
χ594-4-444-44-400000000000000−2i22i22i2−2i20000000000000022−220000−2i2i2i−2i000000000000000
χ604-4-444-44-400000000000000−2i22i22i2−2i200000000000000−222200002i−2i−2i2i000000000000000
χ614-4-4-444-44004-4-40040000000000000000000000000000000000000000000022−22000
χ624-4-4-444-44004-4-400400000000000000000000000000000000000000000000−2222000
χ634-4-4-444-4400-44400-4000000000000004i−4i000000000000000000000000000000000
χ644-4-4-444-4400-44400-400000000000000−4i4i000000000000000000000000000000000
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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