Finite Group Databasebeta

← Group #282749

Character table — Group #282749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-111-11111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-111111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ172222222222-2-2-2-2222222-20000-2000022220022-2-200000000-2-20000000000000-20000000
χ182222222222-2-2-2-2222222-20000-20000-2-2-2-200-2-2-2-20000000022000000000000020000000
χ192222222222-2-2-2-222-2-2-2-2-20000-20000222200-2-22200000000-2-2000000000000020000000
χ202222222222-2-2-2-222-2-2-2-2-20000-20000-2-2-2-200222200000000220000000000000-20000000
χ2122222222-2-22222-2-20000-22222-222220000-2-2000022-2-200000000000000-2000000000000
χ2222222222-2-22222-2-20000-22222-2-2-2-2-20000-2-20000-2-222000000000000002000000000000
χ2322222222-2-22222-2-20000-2-2-2-2-2-222220000220000-2-2-2-2000000000000002000000000000
χ2422222222-2-22222-2-20000-2-2-2-2-2-2-2-2-2-20000220000222200000000000000-2000000000000
χ2522-22-2-22-2002-22-200000002i2i−2i−2i022-2-2i2i2−i2−i20000002i−2i000000i2−i222−2−2i2i2−i2−i200000000002−20
χ2622-22-2-22-2002-22-200000002i2i−2i−2i022-2-2−i2−i2i2i20000002i−2i000000−i2i2−2−222−i2−i2i2i20000000000−220
χ2722-22-2-22-2002-22-200000002i2i−2i−2i0-2-222i2i2−i2−i2000000−2i2i000000i2−i222−2−2−i2−i2i2i20000000000−220
χ2822-22-2-22-2002-22-200000002i2i−2i−2i0-2-222−i2−i2i2i2000000−2i2i000000−i2i2−2−222i2i2−i2−i200000000002−20
χ2922-22-2-22-2002-22-20000000−2i−2i2i2i022-2-2i2i2−i2−i2000000−2i2i000000i2−i2−2−222i2i2−i2−i20000000000−220
χ3022-22-2-22-2002-22-20000000−2i−2i2i2i022-2-2−i2−i2i2i2000000−2i2i000000−i2i222−2−2−i2−i2i2i200000000002−20
χ3122-22-2-22-2002-22-20000000−2i−2i2i2i0-2-222i2i2−i2−i20000002i−2i000000i2−i2−2−222−i2−i2i2i200000000002−20
χ3222-22-2-22-2002-22-20000000−2i−2i2i2i0-2-222−i2−i2i2i20000002i−2i000000−i2i222−2−2i2i2−i2−i20000000000−220
χ332-222-2-2-222-200002-222-2-2000000i2−i2i2−i22-22-2002-20000i2−i2i2i2−i2−i2000000i2−i2i2−i200000000i2−i2000
χ342-222-2-2-222-200002-222-2-2000000i2−i2i2−i2-22-2200-220000i2−i2i2i2−i2−i2000000−i2i2−i2i200000000−i2i2000
χ352-222-2-2-222-200002-222-2-2000000−i2i2−i2i22-22-2002-20000−i2i2−i2−i2i2i2000000−i2i2−i2i200000000−i2i2000
χ362-222-2-2-222-200002-222-2-2000000−i2i2−i2i2-22-2200-220000−i2i2−i2−i2i2i2000000i2−i2i2−i200000000i2−i2000
χ372-222-2-2-222-200002-2-2-222000000i2−i2i2−i22-22-200-220000i2−i2−i2−i2i2i2000000i2−i2i2−i200000000−i2i2000
χ382-222-2-2-222-200002-2-2-222000000i2−i2i2−i2-22-22002-20000i2−i2−i2−i2i2i2000000−i2i2−i2i200000000i2−i2000
χ392-222-2-2-222-200002-2-2-222000000−i2i2−i2i22-22-200-220000−i2i2i2i2−i2−i2000000−i2i2−i2i200000000i2−i2000
χ402-222-2-2-222-200002-2-2-222000000−i2i2−i2i2-22-22002-20000−i2i2i2i2−i2−i2000000i2−i2i2−i200000000−i2i2000
χ412-2-2-2-22222222-2-2-2-22i−2i2i−2i-2000020000000000002i−2i00000000002i−2i2i−2i00000000002-200000
χ422-2-2-2-22222222-2-2-2-22i−2i2i−2i-2000020000000000002i−2i0000000000−2i2i−2i2i0000000000-2200000
χ432-2-2-2-22222222-2-2-2-2−2i2i−2i2i-200002000000000000−2i2i00000000002i−2i2i−2i0000000000-2200000
χ442-2-2-2-22222222-2-2-2-2−2i2i−2i2i-200002000000000000−2i2i0000000000−2i2i−2i2i00000000002-200000
χ452-2-2-2-222222-2-222-2-22i−2i2i−2i22-22-2-2000000002-200−2i2i00000000000000000002i−2i0000000000
χ462-2-2-2-222222-2-222-2-22i−2i2i−2i2-22-22-200000000-2200−2i2i0000000000000000000−2i2i0000000000
χ472-2-2-2-222222-2-222-2-2−2i2i−2i2i22-22-2-2000000002-2002i−2i0000000000000000000−2i2i0000000000
χ482-2-2-2-222222-2-222-2-2−2i2i−2i2i2-22-22-200000000-22002i−2i00000000000000000002i−2i0000000000
χ492-2-2-2-2222-2-2-2-222220000-22-22-2200000000-22000000002-22-200000000000002-200000000
χ502-2-2-2-2222-2-2-2-222220000-22-22-2200000000-2200000000-22-220000000000000-2200000000
χ512-2-2-2-2222-2-2-2-222220000-2-22-222000000002-2000000002-22-20000000000000-2200000000
χ522-2-2-2-2222-2-2-2-222220000-2-22-222000000002-200000000-22-2200000000000002-200000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ5444-44-4-44-400-44-4400000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ5544-44-4-44-400-44-440000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ5644-4-44-4-444-40000-444i−4i−4i4i000000000000000000000000000000000000000000000000000
χ5744-4-44-4-444-40000-44−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ5844-4-44-4-44-4400004-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5944-4-44-4-44-4400004-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ604-444-4-4-44-440000-4400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ614-444-4-4-44-440000-440000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ624-44-44-44-4004-4-440000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ634-44-44-44-4004-4-44000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ644-44-44-44-400-444-400000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ654-44-44-44-400-444-40000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ664-4-4444-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ674-4-4444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ684-4-4444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ694-4-4444-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ704-4-4-4-4444-4-444-4-444000040000-4000000000000000000000000000000000000000000000
χ71888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000

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