Finite Group Databasebeta

← Group #10690113

Character table — Group #10690113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222224444444444888888888888888888881616161616161616161624242424242424242424242424242424
order12222222366666664444441212121244448888121212122424242424242424226666121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ91-111-1-11-11-1-1111-1-111-1-1-1111-1-1i−ii−iii−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-1i−i1-1i−iii−i−i11-1-1
χ101-111-1-11-11-1-1111-1-111-1-1-1111-1-1i−ii−iii−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i-11−ii-11−ii−i−iii-1-111
χ111-111-1-11-11-1-1111-1-111-1-1-1111-1-1i−ii−i−i−iii11-1-1−i−i−i−iiiii-11-1-111ii−i−i1-1i−i1-1i−i−i−iii-1-111
χ121-111-1-11-11-1-1111-1-111-1-1-1111-1-1i−ii−i−i−iii11-1-1−i−i−i−iiiii-11-1-111ii−i−i-11−ii-11−iiii−i−i11-1-1
χ131-111-1-11-11-1-1111-1-111-1-1-1111-1-1−ii−iiii−i−i11-1-1iiii−i−i−i−i-11-1-111−i−iii1-1−ii1-1−iiii−i−i-1-111
χ141-111-1-11-11-1-1111-1-111-1-1-1111-1-1−ii−iiii−i−i11-1-1iiii−i−i−i−i-11-1-111−i−iii-11i−i-11i−i−i−iii11-1-1
χ151-111-1-11-11-1-1111-1-111-1-1-1111-1-1−ii−ii−i−iii11-1-1−i−i−i−iiiii1-111-1-1−i−iii1-1−ii1-1−ii−i−iii11-1-1
χ161-111-1-11-11-1-1111-1-111-1-1-1111-1-1−ii−ii−i−iii11-1-1−i−i−i−iiiii1-111-1-1−i−iii-11i−i-11i−iii−i−i-1-111
χ1722222222222222222-2-22-2-2222222-2-20000-2-2-2-2000000000000002-22-20000000000000000
χ1822222222222222222-2-22-2-22222-2-2220000-2-2-2-200000000000000-22-220000000000000000
χ192222222222222222-22-2-22-2-2-2-2-2000000002-22-2000000000000000000002200-2-200000000
χ202222222222222222-22-2-22-2-2-2-2-2000000002-22-200000000000000000000-2-2002200000000
χ212222222222222222-2-22-2-22-2-2-2-200000000-22-220000000000000000002200-2-20000000000
χ222222222222222222-2-22-2-22-2-2-2-200000000-22-22000000000000000000-2-200220000000000
χ2322222222-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ2422222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-21111-1-1-1-10000000000000000
χ2522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ2622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-1-1-1-111110000000000000000
χ2722222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-122-2-200001111−i3−i3i3i3−i3−i3i3i300−i3i3−i3i3-11-110000000000000000
χ2822222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-122-2-200001111i3i3−i3−i3i3i3−i3−i300i3−i3i3−i3-11-110000000000000000
χ2922222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-2-22200001111−i3−i3i3i3−i3−i3i3i300i3−i3i3−i31-11-10000000000000000
χ3022222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-2-22200001111i3i3−i3−i3i3i3−i3−i300−i3i3−i3i31-11-10000000000000000
χ312-222-2-22-22-2-2222-2-22-22-22-222-2-22i−2i−2i2i0000-2-222000000000000002i−2i−2i2i0000000000000000
χ322-222-2-22-22-2-2222-2-22-22-22-222-2-2−2i2i2i−2i0000-2-22200000000000000−2i2i2i−2i0000000000000000
χ332-222-2-22-22-2-2222-2-2-2222-2-2-2-222000000002-2-22000000000000000000002i−2i00−2i2i00000000
χ342-222-2-22-22-2-2222-2-2-2222-2-2-2-222000000002-2-2200000000000000000000−2i2i002i−2i00000000
χ352-222-2-22-22-2-2222-2-2-2-2-2222-2-22200000000-222-20000000000000000002-200-220000000000
χ362-222-2-22-22-2-2222-2-2-2-2-2222-2-22200000000-222-2000000000000000000-22002-20000000000
χ372-222-2-22-2-111-1-1-11122-2-2-22-1-1112i−2i2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii2-2-1-111−i−iii0000000000000000
χ382-222-2-22-2-111-1-1-11122-2-2-22-1-1112i−2i2i−2i−2i−2i2i2i-1-111iiii−i−i−i−i-2211-1-1−i−iii0000000000000000
χ392-222-2-22-2-111-1-1-11122-2-2-22-1-111−2i2i−2i2i2i2i−2i−2i-1-111−i−i−i−iiiii-2211-1-1ii−i−i0000000000000000
χ402-222-2-22-2-111-1-1-11122-2-2-22-1-111−2i2i−2i2i−2i−2i2i2i-1-111iiii−i−i−i−i2-2-1-111ii−i−i0000000000000000
χ412-222-2-22-2-111-1-1-1112-22-22-2-1-1112i−2i−2i2i000011-1-133−3−3−3−33300−i3i3i3−i3−iii−i0000000000000000
χ422-222-2-22-2-111-1-1-1112-22-22-2-1-1112i−2i−2i2i000011-1-1−3−33333−3−300i3−i3−i3i3−iii−i0000000000000000
χ432-222-2-22-2-111-1-1-1112-22-22-2-1-111−2i2i2i−2i000011-1-133−3−3−3−33300i3−i3−i3i3i−i−ii0000000000000000
χ442-222-2-22-2-111-1-1-1112-22-22-2-1-111−2i2i2i−2i000011-1-1−3−33333−3−300−i3i3i3−i3i−i−ii0000000000000000
χ4544444444-2-2-2-2-2-2-2-2-44-4-44-4222200000000-22-220000000000000000000000000000000000
χ4644444444-2-2-2-2-2-2-2-2-4-44-4-442222000000002-22-20000000000000000000000000000000000
χ47444-44-4-4-444-44-4-44-40000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ48444-44-4-4-444-44-4-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ4944-44-44-4-4444-44-4-4-4000000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ5044-44-44-4-4444-44-4-4-400000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ5144-44-44-4-4-2-2-22-2222000000−2i32i3−2i32i300002i−2i2i−2i00002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ5244-44-44-4-4-2-2-22-2222000000−2i32i3−2i32i30000−2i2i−2i2i0000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ5344-44-44-4-4-2-2-22-22220000002i3−2i32i3−2i300002i−2i2i−2i00002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ5444-44-44-4-4-2-2-22-22220000002i3−2i32i3−2i30000−2i2i−2i2i0000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ5544-4-4-4-44444-4-4-44-4400000000000000000000000000000000000000000000000000002-22-2
χ5644-4-4-4-44444-4-4-44-440000000000000000000000000000000000000000000000000000-22-22
χ574-444-4-44-4-222-2-2-222-4444-4-422-2-200000000-222-20000000000000000000000000000000000
χ584-444-4-44-4-222-2-2-222-4-4-444422-2-2000000002-2-220000000000000000000000000000000000
χ594-44-4-44-444-444-4-4-440000000000000000000000000000000000000000000000002-2-220000
χ604-44-4-44-444-444-4-4-44000000000000000000000000000000000000000000000000-222-20000
χ614-4-444-4-444-4-4-44-444000000000000002-2-2200002-22-2-22-2200000000000000000000000000
χ624-4-444-4-444-4-4-44-44400000000000000-222-20000-22-222-22-200000000000000000000000000
χ634-4-444-4-44-2222-22-2-2000000−2i32i32i3−2i300002-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ644-4-444-4-44-2222-22-2-2000000−2i32i32i3−2i30000-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ654-4-444-4-44-2222-22-2-20000002i3−2i3−2i32i300002-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ664-4-444-4-44-2222-22-2-20000002i3−2i3−2i32i30000-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ674-4-4-4444-44-44-4-444-400000000000000000000000000000000000000000000000000002-2-22
χ684-4-4-4444-44-44-4-444-40000000000000000000000000000000000000000000000000000-222-2
χ69888-88-8-8-8-4-44-444-4400000000000000000000000000000000000000000000000000000000
χ7088-8-8-8-888-4-4444-44-400000000000000000000000000000000000000000000000000000000
χ718-88-8-88-88-44-4-4444-400000000000000000000000000000000000000000000000000000000
χ728-8-8-8888-8-44-444-4-4400000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.