Finite Group Databasebeta

← Group #99813

Character table — Group #99813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444888888888888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ911111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−iii
χ1111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-111ii−i−i
χ1211111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii
χ1311111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−i−iii
χ1411111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−i
χ1511111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iii
χ1611111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111ii−i−i
χ1722222222222222-2-2-2-222-2-2-2-222-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222222-2-2-2-222-2-2-2-222-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-22222-2-22222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ20222222222222-2-22222-2-22222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-22222-2-22222-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-22222-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000
χ2522222222-2-2-2-222-2-22222-2-222-2-222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-222-2-22222-2-222-2-222-2-20000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-22200000000000000000000000000000000000000002-2-22
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2220000000000000000000000000000000000000000-222-2
χ2922-2-22-22-22i2i−2i−2i002-22i−2i002-22i−2i000000002i−2i2-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3022-2-22-22-22i2i−2i−2i002-22i−2i002-22i−2i000000002i−2i2-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3122-2-22-22-22i2i−2i−2i002-22i−2i002-22i−2i00000000−2i2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3222-2-22-22-22i2i−2i−2i002-22i−2i002-22i−2i00000000−2i2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3322-2-22-22-2−2i−2i2i2i002-2−2i2i002-2−2i2i000000002i−2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3422-2-22-22-2−2i−2i2i2i002-2−2i2i002-2−2i2i000000002i−2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3522-2-22-22-2−2i−2i2i2i002-2−2i2i002-2−2i2i00000000−2i2i2-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3622-2-22-22-2−2i−2i2i2i002-2−2i2i002-2−2i2i00000000−2i2i2-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ372-22-2-222-22i−2i2i−2i2i−2i2-22i−2i2i−2i-22−2i2i2-22-22i−2i0000000000000000000000000000000000002-22i−2i0000
χ382-22-2-222-22i−2i2i−2i2i−2i2-22i−2i2i−2i-22−2i2i2-22-22i−2i000000000000000000000000000000000000-22−2i2i0000
χ392-22-2-222-22i−2i2i−2i2i−2i-22−2i2i2i−2i2-22i−2i2-2-22−2i2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000
χ402-22-2-222-22i−2i2i−2i2i−2i-22−2i2i2i−2i2-22i−2i2-2-22−2i2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000
χ412-22-2-222-22i−2i2i−2i−2i2i2-22i−2i−2i2i-22−2i2i-22-22−2i2i000000000000000000000000000000002-22i−2i00000000
χ422-22-2-222-22i−2i2i−2i−2i2i2-22i−2i−2i2i-22−2i2i-22-22−2i2i00000000000000000000000000000000-22−2i2i00000000
χ432-22-2-222-22i−2i2i−2i−2i2i-22−2i2i−2i2i2-22i−2i-222-22i−2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ442-22-2-222-22i−2i2i−2i−2i2i-22−2i2i−2i2i2-22i−2i-222-22i−2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ452-22-2-222-2−2i2i−2i2i2i−2i2-2−2i2i2i−2i-222i−2i-22-222i−2i000000000000000000000000000000002-2−2i2i00000000
χ462-22-2-222-2−2i2i−2i2i2i−2i2-2−2i2i2i−2i-222i−2i-22-222i−2i00000000000000000000000000000000-222i−2i00000000
χ472-22-2-222-2−2i2i−2i2i2i−2i-222i−2i2i−2i2-2−2i2i-222-2−2i2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ482-22-2-222-2−2i2i−2i2i2i−2i-222i−2i2i−2i2-2−2i2i-222-2−2i2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ492-22-2-222-2−2i2i−2i2i−2i2i2-2−2i2i−2i2i-222i−2i2-22-2−2i2i0000000000000000000000000000000000002-2−2i2i0000
χ502-22-2-222-2−2i2i−2i2i−2i2i2-2−2i2i−2i2i-222i−2i2-22-2−2i2i000000000000000000000000000000000000-222i−2i0000
χ512-22-2-222-2−2i2i−2i2i−2i2i-222i−2i−2i2i2-2−2i2i2-2-222i−2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000000000
χ522-22-2-222-2−2i2i−2i2i−2i2i-222i−2i−2i2i2-2−2i2i2-2-222i−2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000
χ532-2-22-2-2222-2-2200-2-2-2-20022220000002-200002-22−2−22−222−2000000002−2−22−222−2000000000000
χ542-2-22-2-2222-2-2200-2-2-2-20022220000002-200002-2−222−22−2−2200000000−222−22−2−22000000000000
χ552-2-22-2-2222-2-2200-2-2-2-2002222000000-220000-222−2−22−222−200000000−222−22−2−22000000000000
χ562-2-22-2-2222-2-2200-2-2-2-2002222000000-220000-22−222−22−2−22000000002−2−22−222−2000000000000
χ572-2-22-2-222-222-200-2-2220022-2-20000002-20000-22i2−i2−i2i2i2−i2−i2i200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ582-2-22-2-222-222-200-2-2220022-2-20000002-20000-22−i2i2i2−i2−i2i2i2−i200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ592-2-22-2-222-222-200-2-2220022-2-2000000-2200002-2i2−i2−i2i2i2−i2−i2i200000000−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-22-2-222-222-200-2-2220022-2-2000000-2200002-2−i2i2i2−i2−i2i2i2−i200000000i2−i2−i2i2i2−i2−i2i2000000000000
χ61444-4-4-4-4400004i−4i0000−4i4i00000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ62444-4-4-4-4400004i−4i0000−4i4i0000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ63444-4-4-4-440000−4i4i00004i−4i00000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ64444-4-4-4-440000−4i4i00004i−4i0000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ6544-4-44-44-44i4i−4i−4i00-44−4i4i00-44−4i4i00000000000000000000000000000000000000000000000000
χ6644-4-44-44-4−4i−4i4i4i00-444i−4i00-444i−4i00000000000000000000000000000000000000000000000000
χ674-4444-4-4-40000440000-4-40000000000000000000000000022−22000022−2200000000000000000000
χ684-4444-4-4-40000440000-4-400000000000000000000000000−22220000−222200000000000000000000
χ694-4444-4-4-40000-4-4000044000000000000000000000000002i2−2i20000−2i22i200000000000000000000
χ704-4444-4-4-40000-4-400004400000000000000000000000000−2i22i200002i2−2i200000000000000000000
χ714-4-44-4-4444-4-4400444400-4-4-4-400000000000000000000000000000000000000000000000000
χ724-4-44-4-444-444-40044-4-400-4-44400000000000000000000000000000000000000000000000000
χ7388-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000

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