Finite Group Databasebeta

← Group #274187

Character table — Group #274187

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888822228888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111
χ91111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-11
χ101111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-1
χ111111111111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1111-1
χ121111111111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-111-1-111-1-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-111-1-111-11
χ172222222222-2-22-2-2222-2-222-2-22222-2-2-2-200000000-222-2-200000000000000000000000000
χ182222222222-2-22-2-2222-2-222-2-2-2-2-2-2222200000000-2-2-22200000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-2222222-2-2-2-2000000002-2-22200000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-222-2-2-2-2222200000000222-2-200000000000000000000000000
χ2122222222-2-222-222-222-2-2-2-2-2-2000000002222-2-2-2-220000-2-2220000000000000000000000
χ2222222222-2-222-222-222-2-2-2-2-2-200000000-2-2-2-222222000022-2-20000000000000000000000
χ2322222222-2-222-222-2-2-2-2-222220000000022222222-20000-2-2-2-20000000000000000000000
χ2422222222-2-222-222-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2220000000000000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2220000000000000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292222-2-2-2-22-22-222-2-2002-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000002-200002i−2i0000
χ302222-2-2-2-22-22-222-2-2002-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000-220000−2i2i0000
χ312222-2-2-2-22-22-222-2-2002-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000002-20000−2i2i0000
χ322222-2-2-2-22-22-222-2-2002-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000-2200002i−2i0000
χ332222-2-2-2-22-2-222-22-200-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000002-200002i−2i000000
χ342222-2-2-2-22-2-222-22-200-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000-220000−2i2i000000
χ352222-2-2-2-22-2-222-22-200-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000002-20000−2i2i000000
χ362222-2-2-2-22-2-222-22-200-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000-2200002i−2i000000
χ3722-2-22-2-222200-200-22-2002-2002i−2i2i−2i000022−2−222−2−202i−2i002−22−2i2−i2i2−i2i2−i2i2−i200000000000000
χ3822-2-22-2-222200-200-22-2002-2002i−2i2i−2i0000−2−222−2−22202i−2i00−22−22−i2i2−i2i2−i2i2−i2i200000000000000
χ3922-2-22-2-222200-200-22-2002-200−2i2i−2i2i000022−2−222−2−20−2i2i002−22−2−i2i2−i2i2−i2i2−i2i200000000000000
χ4022-2-22-2-222200-200-22-2002-200−2i2i−2i2i0000−2−222−2−2220−2i2i00−22−22i2−i2i2−i2i2−i2i2−i200000000000000
χ4122-2-22-2-222200-200-2-2200-22002i−2i2i−2i000022−2−2−2−2220−2i2i002−2−22i2−i2i2−i2−i2i2−i2i200000000000000
χ4222-2-22-2-222200-200-2-2200-22002i−2i2i−2i0000−2−22222−2−20−2i2i00−222−2−i2i2−i2i2i2−i2i2−i200000000000000
χ4322-2-22-2-222200-200-2-2200-2200−2i2i−2i2i000022−2−2−2−22202i−2i002−2−22−i2i2−i2i2i2−i2i2−i200000000000000
χ4422-2-22-2-222200-200-2-2200-2200−2i2i−2i2i0000−2−22222−2−202i−2i00−222−2i2−i2i2−i2−i2i2−i2i200000000000000
χ4522-2-22-2-22-2-20020022-200-220000002-22-222−2−2−2−2220002-2−222−22−2−222−2−2200000000000000
χ4622-2-22-2-22-2-20020022-200-220000002-22-2−2−22222−2−20002-22−2−22−222−2−222−200000000000000
χ4722-2-22-2-22-2-20020022-200-22000000-22-2222−2−2−2−222000-22−222−2−222−2−222−200000000000000
χ4822-2-22-2-22-2-20020022-200-22000000-22-22−2−22222−2−2000-222−2−222−2−222−2−2200000000000000
χ4922-2-22-2-22-2-2002002-22002-20000002-22-222−2−222−2−2000-22−22−222−2−22−222−200000000000000
χ5022-2-22-2-22-2-2002002-22002-20000002-22-2−2−222−2−222000-222−22−2−222−22−2−2200000000000000
χ5122-2-22-2-22-2-2002002-22002-2000000-22-2222−2−222−2−20002-2−22−22−222−22−2−2200000000000000
χ5222-2-22-2-22-2-2002002-22002-2000000-22-22−2−222−2−2220002-22−22−22−2−22−222−200000000000000
χ534444-4-4-4-4-444-4-44-4400-44000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-44-44-4-444004-4000000000000000000000000000000000000000000000000000
χ5544-4-4-444-44-400-4004000000004-4-440000000000000000000000000000000000000000000
χ5644-4-4-444-44-400-400400000000-444-40000000000000000000000000000000000000000000
χ5744-4-4-444-4-4400400-40000000000004i−4i−4i4i000000000000000000000000000000000000000
χ5844-4-4-444-4-4400400-4000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ594-44-444-4-400440-4-400000000000000000000000000000000000000000000002i2−2i200000000
χ604-44-444-4-400440-4-40000000000000000000000000000000000000000000000−2i22i200000000
χ614-44-444-4-400-4-4044000000000000000000000000000000000000000000000000000022−2200
χ624-44-444-4-400-4-40440000000000000000000000000000000000000000000000000000−222200
χ634-44-4-4-444004-40-440000000000000000000004-44-40000000000000000000000000000000
χ644-44-4-4-444004-40-44000000000000000000000-44-440000000000000000000000000000000
χ654-44-4-4-44400-4404-4000000000000000004-44-400000000000000000000000000000000000
χ664-44-4-4-44400-4404-400000000000000000-44-4400000000000000000000000000000000000
χ674-4-44-44-44000000000000004-40000000022−22−222222−22−22220000000000000000000000000000000
χ684-4-44-44-44000000000000004-400000000−222222−22−222222−220000000000000000000000000000000
χ694-4-44-44-4400000000000000-440000000022−22−2222−222222−220000000000000000000000000000000
χ704-4-44-44-4400000000000000-4400000000−222222−2222−22−22220000000000000000000000000000000
χ718-8-888-88-8000000000000000000000000000000000000000000000000000000000000000

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