Finite Group Databasebeta

← Group #324648

Character table — Group #324648

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444444444888822448888888888888888888888888844882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-11
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1111-1-11
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11-11
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-11-11
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-11-11-1
χ17222222222-2-222-2-222222-2-2-2-2-2-2000022-2-2000000000000000000000000002-2000000
χ18222222222-2-222-2-222222-2-2-2-2-2-20000-2-22200000000000000000000000000-22000000
χ19222222222-2-222-2-22-2-2-2-22222-2-2000022-2-200000000000000000000000000-22000000
χ20222222222-2-222-2-22-2-2-2-22222-2-20000-2-222000000000000000000000000002-2000000
χ2122222222-222-2-222-222-2-222-2-2-2-22222000022-2-200000000-2-200000000000000000000
χ2222222222-222-2-222-222-2-222-2-2-2-2-2-2-2-20000-2-222000000002200000000000000000000
χ2322222222-222-2-222-2-2-222-2-222-2-222220000-2-22200000000-2-200000000000000000000
χ2422222222-222-2-222-2-2-222-2-222-2-2-2-2-2-2000022-2-2000000002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000002i2i−2i−2i00000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000−2i−2i2i2i0000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000002i2i−2i−2i0000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000−2i−2i2i2i00000000002i−2i0000
χ2922-22-22-2-202-2002-20002i−2i002i−2i0022-2-20000002i−2i22−2−2i2i2−i2−i2000000i2i2−i2−i222−2−200000000
χ3022-22-22-2-202-2002-20002i−2i002i−2i0022-2-20000002i−2i−2−222−i2−i2i2i2000000−i2−i2i2i2−2−22200000000
χ3122-22-22-2-202-2002-20002i−2i002i−2i00-2-222000000−2i2i22−2−2−i2−i2i2i2000000i2i2−i2−i2−2−22200000000
χ3222-22-22-2-202-2002-20002i−2i002i−2i00-2-222000000−2i2i−2−222i2i2−i2−i2000000−i2−i2i2i222−2−200000000
χ3322-22-22-2-202-2002-2000−2i2i00−2i2i0022-2-2000000−2i2i22−2−2−i2−i2i2i2000000−i2−i2i2i222−2−200000000
χ3422-22-22-2-202-2002-2000−2i2i00−2i2i0022-2-2000000−2i2i−2−222i2i2−i2−i2000000i2i2−i2−i2−2−22200000000
χ3522-22-22-2-202-2002-2000−2i2i00−2i2i00-2-2220000002i−2i22−2−2i2i2−i2−i2000000−i2−i2i2i2−2−22200000000
χ3622-22-22-2-202-2002-2000−2i2i00−2i2i00-2-2220000002i−2i−2−222−i2−i2i2i2000000i2i2−i2−i222−2−200000000
χ372-222-2-22-202-200-2202i−2i002i−2i00002i−2i2i−2i00002-2002−22−22−22−2000000i2−i2i2−i2i2−i2i2−i200000000
χ382-222-2-22-202-200-2202i−2i002i−2i00002i−2i2i−2i00002-200−22−22−22−22000000−i2i2−i2i2−i2i2−i2i200000000
χ392-222-2-22-202-200-2202i−2i002i−2i0000−2i2i−2i2i0000-22002−22−2−22−22000000i2−i2i2−i2−i2i2−i2i200000000
χ402-222-2-22-202-200-2202i−2i002i−2i0000−2i2i−2i2i0000-2200−22−222−22−2000000−i2i2−i2i2i2−i2i2−i200000000
χ412-222-2-22-202-200-220−2i2i00−2i2i00002i−2i2i−2i0000-22002−22−2−22−22000000−i2i2−i2i2i2−i2i2−i200000000
χ422-222-2-22-202-200-220−2i2i00−2i2i00002i−2i2i−2i0000-2200−22−222−22−2000000i2−i2i2−i2−i2i2−i2i200000000
χ432-222-2-22-202-200-220−2i2i00−2i2i0000−2i2i−2i2i00002-2002−22−22−22−2000000−i2i2−i2i2−i2i2−i2i200000000
χ442-222-2-22-202-200-220−2i2i00−2i2i0000−2i2i−2i2i00002-200−22−22−22−22000000i2−i2i2−i2i2−i2i2−i200000000
χ452-2-222-2-22222-2-2-2-22000000002-22i−2i−2i2i0000000000002i−2i−2i2i2i−2i0000-222-2000000000000
χ462-2-222-2-22222-2-2-2-22000000002-22i−2i−2i2i000000000000−2i2i2i−2i2i−2i00002-2-22000000000000
χ472-2-222-2-22222-2-2-2-22000000002-2−2i2i2i−2i0000000000002i−2i−2i2i−2i2i00002-2-22000000000000
χ482-2-222-2-22222-2-2-2-22000000002-2−2i2i2i−2i000000000000−2i2i2i−2i−2i2i0000-222-2000000000000
χ492-2-222-2-22-22222-2-2-200000000-222i−2i−2i2i000000002-2-220000−2i2i000000002i−2i−2i2i00000000
χ502-2-222-2-22-22222-2-2-200000000-222i−2i−2i2i00000000-222-20000−2i2i00000000−2i2i2i−2i00000000
χ512-2-222-2-22-22222-2-2-200000000-22−2i2i2i−2i000000002-2-2200002i−2i00000000−2i2i2i−2i00000000
χ522-2-222-2-22-22222-2-2-200000000-22−2i2i2i−2i00000000-222-200002i−2i000000002i−2i−2i2i00000000
χ53444-44-4-4-44004-400-4000000000000004-4000000000000000000000000000000000000
χ54444-44-4-4-44004-400-400000000000000-44000000000000000000000000000000000000
χ55444-44-4-4-4-400-4400400000000000000004i−4i0000000000000000000000000000000000
χ56444-44-4-4-4-400-440040000000000000000−4i4i0000000000000000000000000000000000
χ5744-44-44-4-40-4400-440004i−4i00−4i4i00000000000000000000000000000000000000000000
χ5844-44-44-4-40-4400-44000−4i4i004i−4i00000000000000000000000000000000000000000000
χ594-444-4-44-40-44004-404i−4i00−4i4i0000000000000000000000000000000000000000000000
χ604-444-4-44-40-44004-40−4i4i004i−4i0000000000000000000000000000000000000000000000
χ614-4-444-4-444-4-4-4-444400000000-44000000000000000000000000000000000000000000
χ624-4-444-4-44-4-4-44444-4000000004-4000000000000000000000000000000000000000000
χ634-4-4-4444-4400-4400-4000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ644-4-4-4444-4400-4400-400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ654-4-4-4444-4-4004-40040000000000000000000000000000000022−22−22220000000000000000
χ664-4-4-4444-4-4004-400400000000000000000000000000000000−222222−220000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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