Finite Group Databasebeta

← Group #304112

Character table — Group #304112

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444488888888888888888888888888888161616161616161616163232
order12222222444444444444444422224444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ91111111111111111-1-1-1-11-1-111111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-1-111-1-11-1
χ101111111111111111-1-1-1-11-1-111111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-1-1-111-11
χ111111111111111111-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1-11
χ121111111111111111-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-11-1-1-1-1111-1
χ131111111111111111-1-1-1-11-1-11-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-111-1-111-11
χ141111111111111111-1-1-1-11-1-11-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-11111-1-11-1
χ151111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-1111-1
χ161111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-111111-1-1-11
χ172222222222-2-222-2-22222-2-2-2-20000-2000022-2-20000000000000000-220000000000
χ182222222222-2-222-2-22222-2-2-2-20000-20000-2-22200000000000000002-20000000000
χ192222222222-2-222-2-2-2-2-2-2-222-200002000022220000000000000000-2-20000000000
χ202222222222-2-222-2-2-2-2-2-2-222-2000020000-2-2-2-20000000000000000220000000000
χ2122222222-2-222-2-22222-2-2-222-20000-222220000000000000000000000-2-200000000
χ2222222222-2-222-2-22222-2-2-222-20000-2-2-2-2-200000000000000000000002200000000
χ2322222222-2-222-2-222-2-222-2-2-2-20000222-2-20000000000000000000000-2200000000
χ2422222222-2-222-2-222-2-222-2-2-2-200002-2-22200000000000000000000002-200000000
χ2522222222-2-2-2-2-2-2-2-222-2-22-2-2222-2-2200000000000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22-2-22-2-22220000000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222222-2-2-20000000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-2-222-200000000000000000000000000002-2000000
χ2922-2-222-2-2002-2002-22i−2i0002i−2i0000002-22i−2i000022−2−2i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ3022-2-222-2-2002-2002-22i−2i0002i−2i0000002-22i−2i0000−2−222−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ3122-2-222-2-2002-2002-22i−2i0002i−2i000000-22−2i2i000022−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ3222-2-222-2-2002-2002-22i−2i0002i−2i000000-22−2i2i0000−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ3322-2-222-2-2002-2002-2−2i2i000−2i2i0000002-2−2i2i000022−2−2−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ3422-2-222-2-2002-2002-2−2i2i000−2i2i0000002-2−2i2i0000−2−222i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ3522-2-222-2-2002-2002-2−2i2i000−2i2i000000-222i−2i000022−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ3622-2-222-2-2002-2002-2−2i2i000−2i2i000000-222i−2i0000−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ372-2-22-222-22-22-22-2-220000200-22-22-20000000002i−2i2i−2i0000000000000000002i−2i0000
χ382-2-22-222-22-22-22-2-220000200-22-22-2000000000−2i2i−2i2i000000000000000000−2i2i0000
χ392-2-22-222-22-22-22-2-220000200-2-22-220000000002i−2i2i−2i000000000000000000−2i2i0000
χ402-2-22-222-22-22-22-2-220000200-2-22-22000000000−2i2i−2i2i0000000000000000002i−2i0000
χ412-2-22-222-2-22-22-222-20000200-22-2-2200000000000002i−2i2i−2i00000000000000002i−2i00
χ422-2-22-222-2-22-22-222-20000200-22-2-220000000000000−2i2i−2i2i0000000000000000−2i2i00
χ432-2-22-222-2-22-22-222-20000200-2-222-200000000000002i−2i2i−2i0000000000000000−2i2i00
χ442-2-22-222-2-22-22-222-20000200-2-222-20000000000000−2i2i−2i2i00000000000000002i−2i00
χ4544-44-4-4-444-400-4400000000000000000004i−4i000000000000000000000000000000
χ4644-44-4-4-444-400-440000000000000000000−4i4i000000000000000000000000000000
χ4744-44-4-4-44-44004-40000000000000000000004i−4i0000000000000000000000000000
χ4844-44-4-4-44-44004-4000000000000000000000−4i4i0000000000000000000000000000
χ4944-4-444-4-400-4400-444i−4i000−4i4i000000000000000000000000000000000000000000
χ5044-4-444-4-400-4400-44−4i4i0004i−4i000000000000000000000000000000000000000000
χ514-4444-4-4-44400-4-4000000000000000000000000000000022−2222−220000000000000000
χ524-4444-4-4-44400-4-40000000000000000000000000000000−2222−22220000000000000000
χ534-4444-4-4-4-4-40044000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ544-4444-4-4-4-4-4004400000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ554-44-4-44-44004400-4-40000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ564-44-4-44-44004400-4-4000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ574-44-4-44-4400-4-40044000000000000000000000000022−22−222200000000000000000000
χ584-44-4-44-4400-4-400440000000000000000000000000−222222−2200000000000000000000
χ594-4-44-444-44-4-444-44-40000-400400000000000000000000000000000000000000000
χ604-4-44-444-4-444-4-44-440000-400400000000000000000000000000000000000000000
χ614-4-4-44-44400000000004-400000000000000000000000002-2-222-2-22000000000000
χ624-4-4-44-44400000000004-40000000000000000000000000-222-2-222-2000000000000
χ634-4-4-44-4440000000000-4400000000000000000000000002-2-22-222-2000000000000
χ644-4-4-44-4440000000000-440000000000000000000000000-222-22-2-22000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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