Finite Group Databasebeta

← Group #8402

Character table — Group #8402

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111111122224444444488888888888888888888888888
order1222444422444444444422444444448888888888888888
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1111-11-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1111-11-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-111-11-11-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-111-11-11-1-1-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-11111-1-1-1-111-1-11-11-11-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-11111-1-1-1-111-1-11-11-11-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-11-11ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-11-11−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-1-111-1-111-1-11-1-11-111-1-11ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111-1-111-1-111-1-11-1-11-111-1-11−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-111-1-111-1-111-1-1-111-1-11-111-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-111-1-111-1-1-111-1-11-111-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-22222-2-20000-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-200002200000000000000000000
χ1922222222-2-2-2-22-200002-202020000-2-20000000000000000
χ2022222222-2-2-2-22-200002-20-20-20000220000000000000000
χ2122222222-2-2-2-2-220000-22202000-2-2000000000000000000
χ2222222222-2-2-2-2-220000-22-20-200022000000000000000000
χ232222-2-2-2-222-2-2-2-222-2-2220000-2200000000000000000000
χ242222-2-2-2-222-2-2-2-2-2-2222200002-200000000000000000000
χ252222-2-2-2-2-2-2222-20000-22020-20000-220000000000000000
χ262222-2-2-2-2-2-2222-20000-220-20200002-20000000000000000
χ272222-2-2-2-2-2-222-2200002-220-2000-22000000000000000000
χ282222-2-2-2-2-2-222-2200002-2-2020002-2000000000000000000
χ292-22-22i−2i2i−2i2-22i−2i002-22i−2i000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ302-22-22i−2i2i−2i2-22i−2i002-22i−2i00000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ312-22-22i−2i2i−2i2-22i−2i00-22−2i2i000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ322-22-22i−2i2i−2i2-22i−2i00-22−2i2i00000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ332-22-2−2i2i−2i2i2-2−2i2i002-2−2i2i000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ342-22-2−2i2i−2i2i2-2−2i2i002-2−2i2i00000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ352-22-2−2i2i−2i2i2-2−2i2i00-222i−2i000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ362-22-2−2i2i−2i2i2-2−2i2i00-222i−2i00000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ3744-4-444-4-4000000000000000000000000002-22-200000000
χ3844-4-444-4-400000000000000000000000000-22-2200000000
χ3944-4-4-4-444000000000000000000000000002i−2i−2i2i00000000
χ4044-4-4-4-44400000000000000000000000000−2i2i2i−2i00000000
χ414-44-44i−4i4i−4i-44−4i4i0000000000000000000000000000000000
χ424-44-4−4i4i−4i4i-444i−4i0000000000000000000000000000000000
χ434-4-444i−4i−4i4i00000000000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ444-4-444i−4i−4i4i0000000000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ454-4-44−4i4i4i−4i00000000000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ464-4-44−4i4i4i−4i0000000000000000000000−2ζ2ζ−2ζ32ζ3000000000000

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