Finite Group Databasebeta

← Group #10690123

Character table — Group #10690123

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222224444444444888888888888888888881616161616161616161624242424242424242424242424242424
order122222223666666644444412121212444488881212121224242424242424244412121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ91-111-1-1-111-1-111-1-1111-1-1-1111-1-1i−ii−iii−i−i1-11-1iiii−i−i−i−i1-1ii−i−i11-1-11-1i−ii−i1-1ii−i−i11-1-1
χ101-111-1-1-111-1-111-1-1111-1-1-1111-1-1i−ii−iii−i−i1-11-1iiii−i−i−i−i1-1ii−i−i11-1-1-11−ii−ii-11−i−iii-1-111
χ111-111-1-1-111-1-111-1-1111-1-1-1111-1-1i−ii−i−i−iii1-11-1−i−i−i−iiiii-11ii−i−i-1-1111-1i−ii−i1-1−i−iii-1-111
χ121-111-1-1-111-1-111-1-1111-1-1-1111-1-1i−ii−i−i−iii1-11-1−i−i−i−iiiii-11ii−i−i-1-111-11−ii−ii-11ii−i−i11-1-1
χ131-111-1-1-111-1-111-1-1111-1-1-1111-1-1−ii−iiii−i−i1-11-1iiii−i−i−i−i-11−i−iii-1-1111-1−ii−ii1-1ii−i−i-1-111
χ141-111-1-1-111-1-111-1-1111-1-1-1111-1-1−ii−iiii−i−i1-11-1iiii−i−i−i−i-11−i−iii-1-111-11i−ii−i-11−i−iii11-1-1
χ151-111-1-1-111-1-111-1-1111-1-1-1111-1-1−ii−ii−i−iii1-11-1−i−i−i−iiiii1-1−i−iii11-1-11-1−ii−ii1-1−i−iii11-1-1
χ161-111-1-1-111-1-111-1-1111-1-1-1111-1-1−ii−ii−i−iii1-11-1−i−i−i−iiiii1-1−i−iii11-1-1-11i−ii−i-11ii−i−i-1-111
χ1722222222222222222-2-22-2-2222222-2-20000-2-2-2-200000000002-22-200000000000000000000
χ1822222222222222222-2-22-2-22222-2-2220000-2-2-2-20000000000-22-2200000000000000000000
χ192222222222222222-22-2-22-2-2-2-2-20000000022-2-20000000000000000000022-2-20000000000
χ202222222222222222-22-2-22-2-2-2-2-20000000022-2-200000000000000000000-2-2220000000000
χ212222222222222222-2-22-2-22-2-2-2-200000000-2-222000000000000000000220000-2-200000000
χ222222222222222222-2-22-2-22-2-2-2-200000000-2-222000000000000000000-2-200002200000000
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
χ2422222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-111110000000000000000
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
χ2622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111221111-1-1-1-10000000000000000
χ2722222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-122-2-200001111−i3−i3i3i3−i3−i3i3i300-11-11−i3i3−i3i30000000000000000
χ2822222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-122-2-200001111i3i3−i3−i3i3i3−i3−i300-11-11i3−i3i3−i30000000000000000
χ2922222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-2-22200001111−i3−i3i3i3−i3−i3i3i3001-11-1i3−i3i3−i30000000000000000
χ3022222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-2-22200001111i3i3−i3−i3i3i3−i3−i3001-11-1−i3i3−i3i30000000000000000
χ312-222-2-2-222-2-222-2-222-22-22-222-2-22i−2i−2i2i0000-22-2200000000002i−2i−2i2i00000000000000000000
χ322-222-2-2-222-2-222-2-222-22-22-222-2-2−2i2i2i−2i0000-22-220000000000−2i2i2i−2i00000000000000000000
χ332-222-2-2-222-2-222-2-22-2222-2-2-2-222000000002-2-22000000000000000000002i−2i−2i2i0000000000
χ342-222-2-2-222-2-222-2-22-2222-2-2-2-222000000002-2-2200000000000000000000−2i2i2i−2i0000000000
χ352-222-2-2-222-2-222-2-22-2-2-2222-2-22200000000-222-20000000000000000002-20000-2200000000
χ362-222-2-2-222-2-222-2-22-2-2-2222-2-22200000000-222-2000000000000000000-2200002-200000000
χ372-222-2-2-22-111-1-111-122-2-2-22-1-1112i−2i2i−2i2i2i−2i−2i-11-11−i−i−i−iiiii2-2−i−iii-1-1110000000000000000
χ382-222-2-2-22-111-1-111-122-2-2-22-1-1112i−2i2i−2i−2i−2i2i2i-11-11iiii−i−i−i−i-22−i−iii11-1-10000000000000000
χ392-222-2-2-22-111-1-111-122-2-2-22-1-111−2i2i−2i2i2i2i−2i−2i-11-11−i−i−i−iiiii-22ii−i−i11-1-10000000000000000
χ402-222-2-2-22-111-1-111-122-2-2-22-1-111−2i2i−2i2i−2i−2i2i2i-11-11iiii−i−i−i−i2-2ii−i−i-1-1110000000000000000
χ412-222-2-2-22-111-1-111-12-22-22-2-1-1112i−2i−2i2i00001-11-133−3−3−3−33300−iii−i−i3i3i3−i30000000000000000
χ422-222-2-2-22-111-1-111-12-22-22-2-1-1112i−2i−2i2i00001-11-1−3−33333−3−300−iii−ii3−i3−i3i30000000000000000
χ432-222-2-2-22-111-1-111-12-22-22-2-1-111−2i2i2i−2i00001-11-133−3−3−3−33300i−i−iii3−i3−i3i30000000000000000
χ442-222-2-2-22-111-1-111-12-22-22-2-1-111−2i2i2i−2i00001-11-1−3−33333−3−300i−i−ii−i3i3i3−i30000000000000000
χ4544444444-2-2-2-2-2-2-2-2-44-4-44-4222200000000-2-2220000000000000000000000000000000000
χ4644444444-2-2-2-2-2-2-2-2-4-44-4-4422220000000022-2-20000000000000000000000000000000000
χ47444-44-4-4-444-44-44-4-40000000000000000000000000000000000000000000000002-22-20000
χ48444-44-4-4-444-44-44-4-4000000000000000000000000000000000000000000000000-22-220000
χ4944-44-44-4-4444-44-4-4-4000000000000002-22-200002-22-22-22-200000000000000000000000000
χ5044-44-44-4-4444-44-4-4-400000000000000-22-220000-22-22-22-2200000000000000000000000000
χ5144-44-44-4-4-2-2-22-2222000000−2i32i3−2i32i300002-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ5244-44-44-4-4-2-2-22-2222000000−2i32i3−2i32i30000-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ5344-44-44-4-4-2-2-22-22220000002i3−2i32i3−2i300002-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ5444-44-44-4-4-2-2-22-22220000002i3−2i32i3−2i30000-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ5544-4-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000002-22-2
χ5644-4-4-4-44444-4-4-4-4440000000000000000000000000000000000000000000000000000-22-22
χ574-444-4-4-44-222-2-222-2-4444-4-422-2-200000000-222-20000000000000000000000000000000000
χ584-444-4-4-44-222-2-222-2-4-4-444422-2-2000000002-2-220000000000000000000000000000000000
χ594-44-4-444-44-444-4-44-40000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ604-44-4-444-44-444-4-44-4000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ614-4-444-44-44-4-4-4444-4000000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ624-4-444-44-44-4-4-4444-400000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ634-4-444-44-4-2222-2-2-22000000−2i32i32i3−2i300002i−2i−2i2i00002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ644-4-444-44-4-2222-2-2-22000000−2i32i32i3−2i30000−2i2i2i−2i0000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ654-4-444-44-4-2222-2-2-220000002i3−2i3−2i32i300002i−2i−2i2i00002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ664-4-444-44-4-2222-2-2-220000002i3−2i3−2i32i30000−2i2i2i−2i0000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ674-4-4-444-444-44-4-44-4400000000000000000000000000000000000000000000000000002-2-22
χ684-4-4-444-444-44-4-44-440000000000000000000000000000000000000000000000000000-222-2
χ69888-88-8-8-8-4-44-44-44400000000000000000000000000000000000000000000000000000000
χ7088-8-8-8-888-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ718-88-8-888-8-44-4-444-4400000000000000000000000000000000000000000000000000000000
χ728-8-8-888-88-44-444-44-400000000000000000000000000000000000000000000000000000000

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