Finite Group Databasebeta

← Group #279342

Character table — Group #279342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442222444444444444888888884444488888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-222-22-22222-2-2-2-2-2-22222-2-200000000-222-2-200000000000000000000000000
χ18222222222-2-222-22-22222-2-2-2-2-2-2-2-2-2-222000000002-2-22200000000000000000000000000
χ19222222222-2-222-22-2-2-2-2-22222-2-22222-2-200000000-2-2-22200000000000000000000000000
χ20222222222-2-222-22-2-2-2-2-22222-2-2-2-2-2-22200000000222-2-200000000000000000000000000
χ2122222222-222-2-22-2200000000-2-222-2-2-2-22222-2-2-2-220000-2-2220000000000000000000000
χ2222222222-222-2-22-2200000000-2-222-2-2-2-2-2-2-2-222222000022-2-20000000000000000000000
χ2322222222-222-2-22-2200000000-2-2-2-2222222222222-20000-2-2-2-20000000000000000000000
χ2422222222-222-2-22-2200000000-2-2-2-22222-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-22200000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-22200000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-222-2-200000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-222-2-2-22222-2-2-2-222-2-222-2-22-200000000000000000000000000000002-2002-200000000
χ3022-222-2-2-22222-2-2-2-222-2-222-2-22-20000000000000000000000000000000-2200-2200000000
χ3122-222-2-2-22222-2-2-2-2-2-222-2-2222-200000000000000000000000000000002-200-2200000000
χ3222-222-2-2-22222-2-2-2-2-2-222-2-2222-20000000000000000000000000000000-22002-200000000
χ3322-222-2-2-22-2-22-22-2222-2-2-2-222-220000000000000000000000000000000002i−2i002i−2i000000
χ3422-222-2-2-22-2-22-22-2222-2-2-2-222-22000000000000000000000000000000000−2i2i00−2i2i000000
χ3522-222-2-2-22-2-22-22-22-2-22222-2-2-220000000000000000000000000000000002i−2i00−2i2i000000
χ3622-222-2-2-22-2-22-22-22-2-22222-2-2-22000000000000000000000000000000000−2i2i002i−2i000000
χ3722-2-2-222-2200-2-20202-22-20000002-22-200i2i2−i2−i2i2i2−i2−i202-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ3822-2-2-222-2200-2-20202-22-20000002-22-200−i2−i2i2i2−i2−i2i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ3922-2-2-222-2200-2-20202-22-2000000-22-2200i2i2−i2−i2−i2−i2i2i20-2200i2−i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ4022-2-2-222-2200-2-20202-22-2000000-22-2200−i2−i2i2i2i2i2−i2−i20-2200−i2i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ4122-2-2-222-2200-2-2020-22-220000002-22-200i2i2−i2−i2i2i2−i2−i20-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ4222-2-2-222-2200-2-2020-22-220000002-22-200−i2−i2i2i2−i2−i2i2i20-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ4322-2-2-222-2200-2-2020-22-22000000-22-2200i2i2−i2−i2−i2−i2i2i202-200i2−i2−i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ4422-2-2-222-2200-2-2020-22-22000000-22-2200−i2−i2i2i2i2i2−i2−i202-200−i2i2i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ4522-2-2-222-2-200220-2000002i−2i2i−2i002-2-2200i2i2−i2−i2−i2−i2i2i20002i−2i−i2i2i2−i22−2−222−2−2200000000000000
χ4622-2-2-222-2-200220-2000002i−2i2i−2i002-2-2200−i2−i2i2i2i2i2−i2−i20002i−2ii2−i2−i2i2−222−2−222−200000000000000
χ4722-2-2-222-2-200220-2000002i−2i2i−2i00-222-200i2i2−i2−i2i2i2−i2−i2000−2i2i−i2i2−i2i22−2−22−222−200000000000000
χ4822-2-2-222-2-200220-2000002i−2i2i−2i00-222-200−i2−i2i2i2−i2−i2i2i2000−2i2ii2−i2i2−i2−222−22−2−2200000000000000
χ4922-2-2-222-2-200220-200000−2i2i−2i2i002-2-2200i2i2−i2−i2−i2−i2i2i2000−2i2i−i2i2i2−i2−222−2−222−200000000000000
χ5022-2-2-222-2-200220-200000−2i2i−2i2i002-2-2200−i2−i2i2i2i2i2−i2−i2000−2i2ii2−i2−i2i22−2−222−2−2200000000000000
χ5122-2-2-222-2-200220-200000−2i2i−2i2i00-222-200i2i2−i2−i2i2i2−i2−i20002i−2i−i2i2−i2i2−222−22−2−2200000000000000
χ5222-2-2-222-2-200220-200000−2i2i−2i2i00-222-200−i2−i2i2i2−i2−i2i2i20002i−2ii2−i2i2−i22−2−22−222−200000000000000
χ53444-4-4-4-44400-440-404-4-44000000000000000000000000000000000000000000000000000
χ54444-4-4-4-44400-440-40-444-4000000000000000000000000000000000000000000000000000
χ55444-4-4-4-44-4004-404000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ56444-4-4-4-44-4004-40400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ5744-444-4-4-4-444-44-44-400000000-44000000000000000000000000000000000000000000000
χ5844-444-4-4-4-4-4-4-44444000000004-4000000000000000000000000000000000000000000000
χ594-444-44-4-404-40040-4000000000000000000000000000000000000000000000000022−220000
χ604-444-44-4-404-40040-40000000000000000000000000000000000000000000000000−22220000
χ614-444-44-4-40-4400-4040000000000000000000000000000000000000000000000000002i2−2i200
χ624-444-44-4-40-4400-404000000000000000000000000000000000000000000000000000−2i22i200
χ634-44-44-44-400000000000000000000004i−4i2i2−2i22i2−2i222−2222−220000000000000000000000000000000
χ644-44-44-44-400000000000000000000004i−4i−2i22i2−2i22i2−2222−22220000000000000000000000000000000
χ654-44-44-44-40000000000000000000000−4i4i2i2−2i22i2−2i2−2222−22220000000000000000000000000000000
χ664-44-44-44-40000000000000000000000−4i4i−2i22i2−2i22i222−2222−220000000000000000000000000000000
χ674-4-44-4-44404-400-40400000000000000004-4-4400000000000000000000000000000000000
χ684-4-44-4-44404-400-4040000000000000000-444-400000000000000000000000000000000000
χ694-4-44-4-4440-440040-4000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ704-4-44-4-4440-440040-400000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ718-8-8-888-88000000000000000000000000000000000000000000000000000000000000000

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