Finite Group Databasebeta

← Group #7709

Character table — Group #7709

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11111111222222224444444444888888888888888816161616
order1222222244444444444444444488888888888888884444
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
χ51111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ1011111111-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ1111111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ1211111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ1311111111-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-1-1-1-1-1-1-11111-1-111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-1-1-1-1-1-1-11111-1-111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-2-2-22222-2-2-2-2-2-22200000000000000000000
χ182222222222-2-2-2-222-2-222-2-222-2-200000000000000000000
χ1922222222-2-22222-2-22222-2-2-2-2-2-200000000000000000000
χ2022222222-2-22222-2-2-2-2-2-2-2-2222200000000000000000000
χ2122-2-222-2-22i−2i00002i−2i002i−2i002-2001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ2222-2-222-2-22i−2i00002i−2i002i−2i002-200−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ2322-2-222-2-22i−2i00002i−2i00−2i2i00-22001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ2422-2-222-2-22i−2i00002i−2i00−2i2i00-2200−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ2522-2-222-2-2−2i2i0000−2i2i002i−2i00-22001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ2622-2-222-2-2−2i2i0000−2i2i002i−2i00-2200−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ2722-2-222-2-2−2i2i0000−2i2i00−2i2i002-2001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ2822-2-222-2-2−2i2i0000−2i2i00−2i2i002-200−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ292-22-22-22-22i−2i2i2i−2i−2i−2i2i00002-200000000000000002ζ3−2ζ32ζ−2ζ0000
χ302-22-22-22-22i−2i2i2i−2i−2i−2i2i00002-20000000000000000−2ζ32ζ3−2ζ2ζ0000
χ312-22-22-22-22i−2i−2i−2i2i2i−2i2i0000-220000000000002ζ3−2ζ32ζ−2ζ00000000
χ322-22-22-22-22i−2i−2i−2i2i2i−2i2i0000-22000000000000−2ζ32ζ3−2ζ2ζ00000000
χ332-22-22-22-2−2i2i2i2i−2i−2i2i−2i0000-220000000000002ζ−2ζ2ζ3−2ζ300000000
χ342-22-22-22-2−2i2i2i2i−2i−2i2i−2i0000-22000000000000−2ζ2ζ−2ζ32ζ300000000
χ352-22-22-22-2−2i2i−2i−2i2i2i2i−2i00002-200000000000000002ζ−2ζ2ζ3−2ζ30000
χ362-22-22-22-2−2i2i−2i−2i2i2i2i−2i00002-20000000000000000−2ζ2ζ−2ζ32ζ30000
χ374444-4-4-4-4004-44-400000000000000000000000000000000
χ384444-4-4-4-400-44-4400000000000000000000000000000000
χ3944-4-4-4-44400000000000000004i−4i00000000000000000000
χ4044-4-4-4-4440000000000000000−4i4i00000000000000000000
χ414-44-4-44-44004i−4i−4i4i00000000000000000000000000000000
χ424-44-4-44-4400−4i4i4i−4i00000000000000000000000000000000
χ434-4-444-4-44440000-4-4000000000000000000000000000000
χ444-4-444-4-44-4-4000044000000000000000000000000000000
χ454-4-44-444-4000000004i−4i0000000000000000000000000000
χ464-4-44-444-400000000−4i4i0000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.