Finite Group Databasebeta

← Group #98447

Character table — Group #98447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-111-1-111-11-11-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-111-1-111-11-11-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11-1-1111111-1-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11-1-1111111-1-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-22222-2-2-2-2-2002200-2-20-20200000000000000000000
χ182222222222-2-22222-2-2-2-2-200-2-20022020-200000000000000000000
χ192222222222-2-2-2-2-2-22222-2002200-2-2020-200000000000000000000
χ202222222222-2-2-2-2-2-22222-200-2-200220-20200000000000000000000
χ2122222222-2-22222-2-222-2-2-22200-2-200-202000000000000000000000
χ2222222222-2-22222-2-222-2-2-2-2-200220020-2000000000000000000000
χ2322222222-2-222-2-222-2-222-222002200-20-2000000000000000000000
χ2422222222-2-222-2-222-2-222-2-2-200-2-200202000000000000000000000
χ2522222222-2-2-2-222-2-2-2-22220000000000002-22-20000000000000000
χ2622222222-2-2-2-222-2-2-2-2222000000000000-22-220000000000000000
χ2722222222-2-2-2-2-2-22222-2-220000000000002-2-220000000000000000
χ2822222222-2-2-2-2-2-22222-2-22000000000000-222-20000000000000000
χ2922-2-2-222-2002-2002i−2i002i−2i02i−2i002-200000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ3022-2-2-222-2002-2002i−2i002i−2i02i−2i002-20000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ3122-2-2-222-2002-2002i−2i002i−2i0−2i2i00-2200000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ3222-2-2-222-2002-2002i−2i002i−2i0−2i2i00-220000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ3322-2-2-222-2002-200−2i2i00−2i2i02i−2i00-2200000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ3422-2-2-222-2002-200−2i2i00−2i2i02i−2i00-220000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ3522-2-2-222-2002-200−2i2i00−2i2i0−2i2i002-200000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ3622-2-2-222-2002-200−2i2i00−2i2i0−2i2i002-20000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ37444-4-4-4-44000000004i−4i0000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ38444-4-4-4-44000000004i−4i000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ39444-4-4-4-4400000000−4i4i0000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ40444-4-4-4-4400000000−4i4i000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4144-4-4-444-400-44004i−4i00−4i4i000000000000000000000000000000000
χ4244-4-4-444-400-4400−4i4i004i−4i000000000000000000000000000000000
χ434-444-44-4-400004i−4i000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ444-444-44-4-400004i−4i00000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ454-444-44-4-40000−4i4i000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ464-444-44-4-40000−4i4i00000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ474-44-44-44-44-4000000000000000004i−4i000000000000000000000000
χ484-44-44-44-44-400000000000000000−4i4i000000000000000000000000
χ494-44-44-44-4-4400000000000004i−4i0000000000000000000000000000
χ504-44-44-44-4-440000000000000−4i4i0000000000000000000000000000
χ5188-888-8-8-8000000000000000000000000000000000000000000000
χ528-8-88-8-888000000000000000000000000000000000000000000000
χ538-8-8-888-88000000000000000000000000000000000000000000000

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