Finite Group Databasebeta

← Group #72320869

Character table — Group #72320869

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size112224444448888888816161616161616161616161616161616161632323232112224444448888888816161616161616161616161616161616161632323232
order12244448888161616161616161624888816161616323232323232323224882224444888816161616161616162488881616161632323232323232322488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111-1-111-1-1ii−i−i11-1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i11111-1-111-1-1ii−i−i11-1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ1011111-1-111-1-1ii−i−i11-1-111-1-1i−iii−i−i-1-111−i−iii-11−ii11111-1-111-1-1ii−i−i11-1-111-1-1i−iii−i−i-1-111−i−iii-11−ii
χ1111111-1-111-1-1ii−i−i11-1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii11111-1-111-1-1ii−i−i11-1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ1211111-1-111-1-1ii−i−i11-1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i11111-1-111-1-1ii−i−i11-1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ1311111-1-111-1-1−i−iii11-1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii11111-1-111-1-1−i−iii11-1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ1411111-1-111-1-1−i−iii11-1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i11111-1-111-1-1−i−iii11-1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ1511111-1-111-1-1−i−iii11-1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i11111-1-111-1-1−i−iii11-1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ1611111-1-111-1-1−i−iii11-1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii11111-1-111-1-1−i−iii11-1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ17222222222222222-2-2-2-20000-2-20000000000000000222222222222222-2-2-2-20000-2-20000000000000000
χ1822222222222-2-2-2-2-2-2-2-2000022000000000000000022222222222-2-2-2-2-2-2-2-20000220000000000000000
χ1922222-2-222-2-22i2i−2i−2i-2-2220000−2i2i000000000000000022222-2-222-2-22i2i−2i−2i-2-2220000−2i2i0000000000000000
χ2022222-2-222-2-2−2i−2i2i2i-2-22200002i−2i000000000000000022222-2-222-2-2−2i−2i2i2i-2-22200002i−2i0000000000000000
χ2122-22-22i−2i2-22i−2i00002-22i−2i0000002ζ−2ζ2ζ3−2ζ300000000000022-22-22i−2i2-22i−2i00002-22i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ2222-22-22i−2i2-22i−2i00002-22i−2i000000−2ζ2ζ−2ζ32ζ300000000000022-22-22i−2i2-22i−2i00002-22i−2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ2322-22-22i−2i2-22i−2i0000-22−2i2i2-22i−2i00000000000000000022-22-22i−2i2-22i−2i0000-22−2i2i2-22i−2i000000000000000000
χ2422-22-22i−2i2-22i−2i0000-22−2i2i-22−2i2i00000000000000000022-22-22i−2i2-22i−2i0000-22−2i2i-22−2i2i000000000000000000
χ2522-22-22i−2i-22−2i2i2ζ3−2ζ32ζ−2ζ000000000000002−2i2−i21−i−1+i1+i−1−i000022-22-22i−2i-22−2i2i2ζ3−2ζ32ζ−2ζ000000000000002−2i2−i21−i−1+i1+i−1−i0000
χ2622-22-22i−2i-22−2i2i2ζ3−2ζ32ζ−2ζ00000000000000−22−i2i2−1+i1−i−1−i1+i000022-22-22i−2i-22−2i2i2ζ3−2ζ32ζ−2ζ00000000000000−22−i2i2−1+i1−i−1−i1+i0000
χ2722-22-22i−2i-22−2i2i−2ζ32ζ3−2ζ2ζ000000000000002−2i2−i2−1+i1−i−1−i1+i000022-22-22i−2i-22−2i2i−2ζ32ζ3−2ζ2ζ000000000000002−2i2−i2−1+i1−i−1−i1+i0000
χ2822-22-22i−2i-22−2i2i−2ζ32ζ3−2ζ2ζ00000000000000−22−i2i21−i−1+i1+i−1−i000022-22-22i−2i-22−2i2i−2ζ32ζ3−2ζ2ζ00000000000000−22−i2i21−i−1+i1+i−1−i0000
χ2922-22-2−2i2i2-2−2i2i00002-2−2i2i0000002ζ3−2ζ32ζ−2ζ00000000000022-22-2−2i2i2-2−2i2i00002-2−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ3022-22-2−2i2i2-2−2i2i00002-2−2i2i000000−2ζ32ζ3−2ζ2ζ00000000000022-22-2−2i2i2-2−2i2i00002-2−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ3122-22-2−2i2i2-2−2i2i0000-222i−2i2-2−2i2i00000000000000000022-22-2−2i2i2-2−2i2i0000-222i−2i2-2−2i2i000000000000000000
χ3222-22-2−2i2i2-2−2i2i0000-222i−2i-222i−2i00000000000000000022-22-2−2i2i2-2−2i2i0000-222i−2i-222i−2i000000000000000000
χ3322-22-2−2i2i-222i−2i2ζ−2ζ2ζ3−2ζ3000000000000002−2−i2i2−1−i1+i−1+i1−i000022-22-2−2i2i-222i−2i2ζ−2ζ2ζ3−2ζ3000000000000002−2−i2i2−1−i1+i−1+i1−i0000
χ3422-22-2−2i2i-222i−2i2ζ−2ζ2ζ3−2ζ300000000000000−22i2−i21+i−1−i1−i−1+i000022-22-2−2i2i-222i−2i2ζ−2ζ2ζ3−2ζ300000000000000−22i2−i21+i−1−i1−i−1+i0000
χ3522-22-2−2i2i-222i−2i−2ζ2ζ−2ζ32ζ3000000000000002−2−i2i21+i−1−i1−i−1+i000022-22-2−2i2i-222i−2i−2ζ2ζ−2ζ32ζ3000000000000002−2−i2i21+i−1−i1−i−1+i0000
χ3622-22-2−2i2i-222i−2i−2ζ2ζ−2ζ32ζ300000000000000−22i2−i2−1−i1+i−1+i1−i000022-22-2−2i2i-222i−2i−2ζ2ζ−2ζ32ζ300000000000000−22i2−i2−1−i1+i−1+i1−i0000
χ374444444-4-4-4-40000000000000000000000000000004444444-4-4-4-4000000000000000000000000000000
χ3844444-4-4-4-44400000000000000000000000000000044444-4-4-4-444000000000000000000000000000000
χ39888-8-8000000000000000000000000000000000000888-8-8000000000000000000000000000000000000
χ4088-8-8800000000000000000000000000000000000088-8-88000000000000000000000000000000000000
χ4116-1600000000000000000000000000000000000000016-16000000000000000000000000000000000000000
χ4211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ441111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ451111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1
χ4611111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ4711111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ4811111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ4911111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ5011111-1-111-1-1ii−i−i11-1-111-1-1i−iii−i−i11-1-1ii−i−i1-1i−i-1-1-1-1-111-1-111−i−iii-1-111-1-111−ii−i−iii-1-111−i−iii-11−ii
χ5111111-1-111-1-1ii−i−i11-1-111-1-1i−iii−i−i-1-111−i−iii-11−ii-1-1-1-1-111-1-111−i−iii-1-111-1-111−ii−i−iii11-1-1ii−i−i1-1i−i
χ5211111-1-111-1-1ii−i−i11-1-1-1-111i−i−i−iii11-1-1ii−i−i-11−ii-1-1-1-1-111-1-111−i−iii-1-11111-1-1−iiii−i−i-1-111−i−iii1-1i−i
χ5311111-1-111-1-1ii−i−i11-1-1-1-111i−i−i−iii-1-111−i−iii1-1i−i-1-1-1-1-111-1-111−i−iii-1-11111-1-1−iiii−i−i11-1-1ii−i−i-11−ii
χ5411111-1-111-1-1−i−iii11-1-111-1-1−ii−i−iii11-1-1−i−iii1-1−ii-1-1-1-1-111-1-111ii−i−i-1-111-1-111i−iii−i−i-1-111ii−i−i-11i−i
χ5511111-1-111-1-1−i−iii11-1-111-1-1−ii−i−iii-1-111ii−i−i-11i−i-1-1-1-1-111-1-111ii−i−i-1-111-1-111i−iii−i−i11-1-1−i−iii1-1−ii
χ5611111-1-111-1-1−i−iii11-1-1-1-111−iiii−i−i11-1-1−i−iii-11i−i-1-1-1-1-111-1-111ii−i−i-1-11111-1-1i−i−i−iii-1-111ii−i−i1-1−ii
χ5711111-1-111-1-1−i−iii11-1-1-1-111−iiii−i−i-1-111ii−i−i1-1−ii-1-1-1-1-111-1-111ii−i−i-1-11111-1-1i−i−i−iii11-1-1−i−iii-11i−i
χ58222222222222222-2-2-2-20000-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000220000000000000000
χ5922222222222-2-2-2-2-2-2-2-20000220000000000000000-2-2-2-2-2-2-2-2-2-2-2222222220000-2-20000000000000000
χ6022222-2-222-2-22i2i−2i−2i-2-2220000−2i2i0000000000000000-2-2-2-2-222-2-222−2i−2i2i2i22-2-200002i−2i0000000000000000
χ6122222-2-222-2-2−2i−2i2i2i-2-22200002i−2i0000000000000000-2-2-2-2-222-2-2222i2i−2i−2i22-2-20000−2i2i0000000000000000
χ6222-22-22i−2i2-22i−2i00002-22i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000-2-22-22−2i2i-22−2i2i0000-22−2i2i000000−2ζ2ζ−2ζ32ζ3000000000000
χ6322-22-22i−2i2-22i−2i00002-22i−2i000000−2ζ2ζ−2ζ32ζ3000000000000-2-22-22−2i2i-22−2i2i0000-22−2i2i0000002ζ−2ζ2ζ3−2ζ3000000000000
χ6422-22-22i−2i2-22i−2i0000-22−2i2i2-22i−2i000000000000000000-2-22-22−2i2i-22−2i2i00002-22i−2i-22−2i2i000000000000000000
χ6522-22-22i−2i2-22i−2i0000-22−2i2i-22−2i2i000000000000000000-2-22-22−2i2i-22−2i2i00002-22i−2i2-22i−2i000000000000000000
χ6622-22-22i−2i-22−2i2i2ζ3−2ζ32ζ−2ζ000000000000002−2i2−i21−i−1+i1+i−1−i0000-2-22-22−2i2i2-22i−2i−2ζ32ζ3−2ζ2ζ00000000000000−22−i2i2−1+i1−i−1−i1+i0000
χ6722-22-22i−2i-22−2i2i2ζ3−2ζ32ζ−2ζ00000000000000−22−i2i2−1+i1−i−1−i1+i0000-2-22-22−2i2i2-22i−2i−2ζ32ζ3−2ζ2ζ000000000000002−2i2−i21−i−1+i1+i−1−i0000
χ6822-22-22i−2i-22−2i2i−2ζ32ζ3−2ζ2ζ000000000000002−2i2−i2−1+i1−i−1−i1+i0000-2-22-22−2i2i2-22i−2i2ζ3−2ζ32ζ−2ζ00000000000000−22−i2i21−i−1+i1+i−1−i0000
χ6922-22-22i−2i-22−2i2i−2ζ32ζ3−2ζ2ζ00000000000000−22−i2i21−i−1+i1+i−1−i0000-2-22-22−2i2i2-22i−2i2ζ3−2ζ32ζ−2ζ000000000000002−2i2−i2−1+i1−i−1−i1+i0000
χ7022-22-2−2i2i2-2−2i2i00002-2−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000-2-22-222i−2i-222i−2i0000-222i−2i000000−2ζ32ζ3−2ζ2ζ000000000000
χ7122-22-2−2i2i2-2−2i2i00002-2−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000-2-22-222i−2i-222i−2i0000-222i−2i0000002ζ3−2ζ32ζ−2ζ000000000000
χ7222-22-2−2i2i2-2−2i2i0000-222i−2i2-2−2i2i000000000000000000-2-22-222i−2i-222i−2i00002-2−2i2i-222i−2i000000000000000000
χ7322-22-2−2i2i2-2−2i2i0000-222i−2i-222i−2i000000000000000000-2-22-222i−2i-222i−2i00002-2−2i2i2-2−2i2i000000000000000000
χ7422-22-2−2i2i-222i−2i2ζ−2ζ2ζ3−2ζ3000000000000002−2−i2i2−1−i1+i−1+i1−i0000-2-22-222i−2i2-2−2i2i−2ζ2ζ−2ζ32ζ300000000000000−22i2−i21+i−1−i1−i−1+i0000
χ7522-22-2−2i2i-222i−2i2ζ−2ζ2ζ3−2ζ300000000000000−22i2−i21+i−1−i1−i−1+i0000-2-22-222i−2i2-2−2i2i−2ζ2ζ−2ζ32ζ3000000000000002−2−i2i2−1−i1+i−1+i1−i0000
χ7622-22-2−2i2i-222i−2i−2ζ2ζ−2ζ32ζ3000000000000002−2−i2i21+i−1−i1−i−1+i0000-2-22-222i−2i2-2−2i2i2ζ−2ζ2ζ3−2ζ300000000000000−22i2−i2−1−i1+i−1+i1−i0000
χ7722-22-2−2i2i-222i−2i−2ζ2ζ−2ζ32ζ300000000000000−22i2−i2−1−i1+i−1+i1−i0000-2-22-222i−2i2-2−2i2i2ζ−2ζ2ζ3−2ζ3000000000000002−2−i2i21+i−1−i1−i−1+i0000
χ784444444-4-4-4-4000000000000000000000000000000-4-4-4-4-4-4-44444000000000000000000000000000000
χ7944444-4-4-4-444000000000000000000000000000000-4-4-4-4-44444-4-4000000000000000000000000000000
χ80888-8-8000000000000000000000000000000000000-8-8-888000000000000000000000000000000000000
χ8188-8-88000000000000000000000000000000000000-8-888-8000000000000000000000000000000000000
χ8216-16000000000000000000000000000000000000000-1616000000000000000000000000000000000000000

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