Finite Group Databasebeta

← Group #499596

Character table — Group #499596

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order124422244488888888888844448824448888161616161616161616161616161616162444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111
χ111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ121111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ17222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-200000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222200000000000000000000000000000000
χ2122222-2-22-2-22222-2-2-2-20000000000002i−2i002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ2222222-2-22-2-22222-2-2-2-20000000000002i−2i002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ2322222-2-22-2-22222-2-2-2-2000000000000−2i2i00−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ2422222-2-22-2-22222-2-2-2-2000000000000−2i2i00−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ2522222-2-22-2-2-2-2-2-222220000000000002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ2622222-2-22-2-2-2-2-2-222220000000000002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ2722222-2-22-2-2-2-2-2-22222000000000000−2i2i002i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ2822222-2-22-2-2-2-2-2-22222000000000000−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ292222-22-2-22-222-2-222-2-2222222-2-2-2-2000000000000000000000000002i−2i0000002i−2i0000
χ302222-22-2-22-222-2-222-2-2222222-2-2-2-200000000000000000000000000−2i2i000000−2i2i0000
χ312222-22-2-22-222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000002i−2i0000002i−2i
χ322222-22-2-22-222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000−2i2i000000−2i2i
χ332222-22-2-22-2-2-222-2-2222222-2-222-2-2000000000000000000000000002i−2i000000−2i2i0000
χ342222-22-2-22-2-2-222-2-2222222-2-222-2-200000000000000000000000000−2i2i0000002i−2i0000
χ352222-22-2-22-2-2-222-2-222-2-2-2-222-2-2220000000000000000000000000000002i−2i000000−2i2i
χ362222-22-2-22-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000000000−2i2i0000002i−2i
χ3722-2-22-2-2-2222i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i2-200000000000000000000000000002i−2i0000002-200
χ3822-2-22-2-2-2222i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i2-20000000000000000000000000000−2i2i000000-2200
χ3922-2-22-2-2-2222i−2i2i−2i2i−2i2i−2i-2-222−2i2i−2i2i-220000000000000000000000002-20000002i−2i000000
χ4022-2-22-2-2-2222i−2i2i−2i2i−2i2i−2i-2-222−2i2i−2i2i-22000000000000000000000000-22000000−2i2i000000
χ4122-2-22-2-2-222−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i2-200000000000000000000000000002i−2i000000-2200
χ4222-2-22-2-2-222−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i2-20000000000000000000000000000−2i2i0000002-200
χ4322-2-22-2-2-222−2i2i−2i2i−2i2i−2i2i-2-2222i−2i2i−2i-220000000000000000000000002-2000000−2i2i000000
χ4422-2-22-2-2-222−2i2i−2i2i−2i2i−2i2i-2-2222i−2i2i−2i-22000000000000000000000000-220000002i−2i000000
χ4522-2-2-22-22-222i−2i−2i2i−2i2i2i−2i00000000002-2002i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000000000
χ4622-2-2-22-22-222i−2i−2i2i−2i2i2i−2i00000000002-2002i−2i00−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000000000
χ4722-2-2-22-22-222i−2i−2i2i−2i2i2i−2i0000000000-2200−2i2i00i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000000000
χ4822-2-2-22-22-222i−2i−2i2i−2i2i2i−2i0000000000-2200−2i2i00−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000000000
χ4922-2-2-22-22-22−2i2i2i−2i2i−2i−2i2i00000000002-200−2i2i00i2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000000000
χ5022-2-2-22-22-22−2i2i2i−2i2i−2i−2i2i00000000002-200−2i2i00−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000000000
χ5122-2-2-22-22-22−2i2i2i−2i2i−2i−2i2i0000000000-22002i−2i00i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000000000
χ5222-2-2-22-22-22−2i2i2i−2i2i−2i−2i2i0000000000-22002i−2i00−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000000000
χ5322-2-2-2-2222-22i−2i−2i2i2i−2i−2i2i22-2-22i−2i−2i2i-22000000002-2-22−2i2i2i−2i000000000000000000000000
χ5422-2-2-2-2222-22i−2i−2i2i2i−2i−2i2i22-2-22i−2i−2i2i-2200000000-222-22i−2i−2i2i000000000000000000000000
χ5522-2-2-2-2222-22i−2i−2i2i2i−2i−2i2i-2-222−2i2i2i−2i2-200000000000000002i−2i−2i2i2-2-220000000000000000
χ5622-2-2-2-2222-22i−2i−2i2i2i−2i−2i2i-2-222−2i2i2i−2i2-20000000000000000−2i2i2i−2i-222-20000000000000000
χ5722-2-2-2-2222-2−2i2i2i−2i−2i2i2i−2i22-2-2−2i2i2i−2i-22000000002-2-222i−2i−2i2i000000000000000000000000
χ5822-2-2-2-2222-2−2i2i2i−2i−2i2i2i−2i22-2-2−2i2i2i−2i-2200000000-222-2−2i2i2i−2i000000000000000000000000
χ5922-2-2-2-2222-2−2i2i2i−2i−2i2i2i−2i-2-2222i−2i−2i2i2-200000000000000002i−2i−2i2i-222-20000000000000000
χ6022-2-2-2-2222-2−2i2i2i−2i−2i2i2i−2i-2-2222i−2i−2i2i2-20000000000000000−2i2i2i−2i2-2-220000000000000000
χ614444-4-44-4-4444-4-4-4-44400000000000000000000000000000000000000000000000000
χ624444-4-44-4-44-4-44444-4-400000000000000000000000000000000000000000000000000
χ6344-4-4444-4-4-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6444-4-4444-4-4-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ658-88i−8i000000000000004i2−4i242−420000000000000000000000000000000000000000000000
χ668-88i−8i00000000000000−4i24i2−42420000000000000000000000000000000000000000000000
χ678-8−8i8i000000000000004i2−4i2−42420000000000000000000000000000000000000000000000
χ688-8−8i8i00000000000000−4i24i242−420000000000000000000000000000000000000000000000

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