Finite Group Databasebeta

← Group #99994

Character table — Group #99994

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444888888888888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ911111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ1011111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1ii−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-111−i−iii-1-111
χ1111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1−i−iiiiiii−i−i−i−i−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111
χ1211111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ1311111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111ii−i−iiiii−i−i−i−iii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1
χ1411111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111
χ1511111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111
χ1611111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−iii−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000222200000000-2-2-2-200000000000000000000
χ202222222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000-2-2-2-200000000222200000000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-222-2-222-2-222-2-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-222-2-222-2-222-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-22222-2-222-2-200000000000000000000000022-2-2-2-222000000000000
χ2622222222-2-2-2-22222-2-2-2-22222-2-222-2-2000000000000000000000000-2-22222-2-2000000000000
χ2722222222-2-2-2-222-2-2-2-2-2-222-2-222-2-222000000002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-222-2-2-2-2-2-222-2-222-2-22200000000−2i−2i2i2i000000002i2i−2i−2i00000000000000000000
χ2922-2-222-2-22i−2i2-22i−2i002i−2i2-22i−2i00000000002-2002i−2i1+i−1−i1−i−1+i000000001+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3022-2-222-2-22i−2i2-22i−2i002i−2i2-22i−2i00000000002-2002i−2i−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3122-2-222-2-22i−2i2-22i−2i002i−2i2-22i−2i0000000000-2200−2i2i1+i−1−i1−i−1+i000000001+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3222-2-222-2-22i−2i2-22i−2i002i−2i2-22i−2i0000000000-2200−2i2i−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3322-2-222-2-22i−2i-22−2i2i002i−2i-22−2i2i000000002i−2i002-2001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ3422-2-222-2-22i−2i-22−2i2i002i−2i-22−2i2i000000002i−2i002-200−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ3522-2-222-2-22i−2i-22−2i2i002i−2i-22−2i2i00000000−2i2i00-22001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ3622-2-222-2-22i−2i-22−2i2i002i−2i-22−2i2i00000000−2i2i00-2200−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ3722-2-222-2-2−2i2i2-2−2i2i00−2i2i2-2−2i2i00000000002-200−2i2i1−i−1+i1+i−1−i000000001−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3822-2-222-2-2−2i2i2-2−2i2i00−2i2i2-2−2i2i00000000002-200−2i2i−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3922-2-222-2-2−2i2i2-2−2i2i00−2i2i2-2−2i2i0000000000-22002i−2i1−i−1+i1+i−1−i000000001−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4022-2-222-2-2−2i2i2-2−2i2i00−2i2i2-2−2i2i0000000000-22002i−2i−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4122-2-222-2-2−2i2i-222i−2i00−2i2i-222i−2i000000002i−2i00-22001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ4222-2-222-2-2−2i2i-222i−2i00−2i2i-222i−2i000000002i−2i00-2200−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ4322-2-222-2-2−2i2i-222i−2i00−2i2i-222i−2i00000000−2i2i002-2001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ4422-2-222-2-2−2i2i-222i−2i00−2i2i-222i−2i00000000−2i2i002-200−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ452-22-22-22-22i−2i2-22i−2i2i−2i−2i2i-22−2i2i2i−2i2-22-22i−2i0000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000
χ462-22-22-22-22i−2i2-22i−2i2i−2i−2i2i-22−2i2i2i−2i2-22-22i−2i000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000
χ472-22-22-22-22i−2i2-22i−2i−2i2i−2i2i-22−2i2i−2i2i-22-22−2i2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ482-22-22-22-22i−2i2-22i−2i−2i2i−2i2i-22−2i2i−2i2i-22-22−2i2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ492-22-22-22-22i−2i-22−2i2i2i−2i−2i2i2-22i−2i2i−2i2-2-22−2i2i00000000000000000000000000000000000000002-22i−2i
χ502-22-22-22-22i−2i-22−2i2i2i−2i−2i2i2-22i−2i2i−2i2-2-22−2i2i0000000000000000000000000000000000000000-22−2i2i
χ512-22-22-22-22i−2i-22−2i2i−2i2i−2i2i2-22i−2i−2i2i-222-22i−2i000000000000000000000000000000002-22i−2i00000000
χ522-22-22-22-22i−2i-22−2i2i−2i2i−2i2i2-22i−2i−2i2i-222-22i−2i00000000000000000000000000000000-22−2i2i00000000
χ532-22-22-22-2−2i2i2-2−2i2i2i−2i2i−2i-222i−2i2i−2i-22-222i−2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ542-22-22-22-2−2i2i2-2−2i2i2i−2i2i−2i-222i−2i2i−2i-22-222i−2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ552-22-22-22-2−2i2i2-2−2i2i−2i2i2i−2i-222i−2i−2i2i2-22-2−2i2i0000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ562-22-22-22-2−2i2i2-2−2i2i−2i2i2i−2i-222i−2i−2i2i2-22-2−2i2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ572-22-22-22-2−2i2i-222i−2i2i−2i2i−2i2-2−2i2i2i−2i-222-2−2i2i000000000000000000000000000000002-2−2i2i00000000
χ582-22-22-22-2−2i2i-222i−2i2i−2i2i−2i2-2−2i2i2i−2i-222-2−2i2i00000000000000000000000000000000-222i−2i00000000
χ592-22-22-22-2−2i2i-222i−2i−2i2i2i−2i2-2−2i2i−2i2i2-2-222i−2i00000000000000000000000000000000000000002-2−2i2i
χ602-22-22-22-2−2i2i-222i−2i−2i2i2i−2i2-2−2i2i−2i2i2-2-222i−2i0000000000000000000000000000000000000000-222i−2i
χ6144-4-4-4-44400000044000000-4-40000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ6244-4-4-4-44400000044000000-4-4000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ6344-4-4-4-444000000-4-4000000440000000000000000002-22-2-22-22000000000000000000000000
χ6444-4-4-4-444000000-4-400000044000000000000000000-22-222-22-2000000000000000000000000
χ654-4-444-4-4444444400-4-4-4-4-4-40000000000000000000000000000000000000000000000000000
χ664-4-444-4-4444-4-4-4-400-4-444440000000000000000000000000000000000000000000000000000
χ674-4-444-4-44-4-444-4-40044-4-4440000000000000000000000000000000000000000000000000000
χ684-4-444-4-44-4-4-4-444004444-4-40000000000000000000000000000000000000000000000000000
χ694-4-44-444-40000004i−4i000000−4i4i0000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ704-4-44-444-40000004i−4i000000−4i4i000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ714-4-44-444-4000000−4i4i0000004i−4i0000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ724-4-44-444-4000000−4i4i0000004i−4i000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ738888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000

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