Finite Group Databasebeta

← Group #8689

Character table — Group #8689

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222222244444444888888888888888816161616
order1222224444444488884488888844448888888888888888
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-111-11-1-11-111111-1-1-111-1-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ101111-1-111-11-1-11-111111-1-1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii
χ111111-1-111-11-1-11-111111-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ121111-1-111-11-1-11-111111-1-1-111-1-1-1-111-1-111−i−iii−i−iiii−ii−i
χ131111-1-111-11-1-11-1-1-1-1-11-111-1-11111-1-1-1-111ii−i−i−i−iiii−i−ii
χ141111-1-111-11-1-11-1-1-1-1-11-111-1-11111-1-1-1-111−i−iiiii−i−i−iii−i
χ151111-1-111-11-1-11-1-1-1-1-11-111-1-111-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111-1-111-11-1-11-1-1-1-1-11-111-1-111-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222-2-2-2-220000-2-200000000002i−2i2i−2i000000000000
χ18222222222-2-2-2-220000-2-20000000000−2i2i−2i2i000000000000
χ19222222-2-2-22222-22222-2-222-2-2-2-200000000000000000000
χ20222222-2-2-22222-2-2-2-2-2-2-2-2-2222200000000000000000000
χ21222222-2-2-2-2-2-2-2-20000220000002-22-20000000000000000
χ22222222-2-2-2-2-2-2-2-2000022000000-22-220000000000000000
χ232222-2-222-2-222-2-20000-2200000000002i−2i−2i2i000000000000
χ242222-2-222-2-222-2-20000-220000000000−2i2i2i−2i000000000000
χ252222-2-2-2-222-2-2222222-22-2-2-2-22200000000000000000000
χ262222-2-2-2-222-2-222-2-2-2-2-222222-2-200000000000000000000
χ272222-2-2-2-22-222-2200002-20000002-2-220000000000000000
χ282222-2-2-2-22-222-2200002-2000000-222-20000000000000000
χ2922-2-22-2000-22-2202i2i−2i−2i002i−2i000000000000i2−i2i2−i22−22−20000
χ3022-2-22-2000-22-2202i2i−2i−2i002i−2i000000000000−i2i2−i2i2−22−220000
χ3122-2-22-2000-22-220−2i−2i2i2i00−2i2i000000000000i2−i2i2−i2−22−220000
χ3222-2-22-2000-22-220−2i−2i2i2i00−2i2i000000000000−i2i2−i2i22−22−20000
χ3322-2-2-22000-2-22202i2i−2i−2i00−2i2i0000000000002−2−22−i2i2i2−i20000
χ3422-2-2-22000-2-22202i2i−2i−2i00−2i2i000000000000−222−2i2−i2−i2i20000
χ3522-2-2-22000-2-2220−2i−2i2i2i002i−2i0000000000002−2−22i2−i2−i2i20000
χ3622-2-2-22000-2-2220−2i−2i2i2i002i−2i000000000000−222−2−i2i2i2−i20000
χ3744-4-44-40004-44-4000000000000000000000000000000000
χ3844-4-4-4400044-4-4000000000000000000000000000000000
χ394-44-4000040000-422−2222−2200000022−2200000000000000000000
χ404-44-4000040000-4−2222−2222000000−222200000000000000000000
χ414-44-40000-40000422−2222−22000000−222200000000000000000000
χ424-44-40000-400004−2222−222200000022−2200000000000000000000
χ434-4-44004i−4i0000002i2−2i2−2i22i2000022−220000000000000000000000
χ444-4-44004i−4i000000−2i22i22i2−2i20000−22220000000000000000000000
χ454-4-4400−4i4i0000002i2−2i2−2i22i20000−22220000000000000000000000
χ464-4-4400−4i4i000000−2i22i22i2−2i2000022−220000000000000000000000

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