Finite Group Databasebeta

← Group #10699159

Character table — Group #10699159

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122234444666244446612121212121212128888121224242424242424242466881212242424248888448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ9222222222222-2-2-2-22-2-222-2-22-2-2200002-2000000000000000000000000002-200
χ10222222222222-2-2-2-22-2-222-2-22-2-2200002-200000000000000000000000000-2200
χ112222222-2-22222-2-22-22222-2-2-2-2-2-22i2i−2i−2i-222i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ122222222-2-22222-2-22-22222-2-2-2-2-2-2−2i−2i2i2i-22−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ132222222-2-2222-222-2-2-2-22222-222-20000-2-200000000000000000000000000002i−2i
χ142222222-2-2222-222-2-2-2-22222-222-20000-2-20000000000000000000000000000−2i2i
χ1522222-2-2222222-22-2-222-2-2-2-222220000-2-2000000002-22200-2-200000000000000
χ1622222-2-2222222-22-2-222-2-2-2-222220000-2-200000000-22-2-2002200000000000000
χ1722222-2-222222-22-22-2-2-2-2-2222-2-220000-220000000000000000000000002-20000
χ1822222-2-222222-22-22-2-2-2-2-2222-2-220000-22000000000000000000000000-220000
χ1922222-2-2-2-222222-2-2222-2-222-2-2-2-200002-20000000000002i−2i002i2i−2i−2i0000000000
χ2022222-2-2-2-222222-2-2222-2-222-2-2-2-200002-2000000000000−2i2i00−2i−2i2i2i0000000000
χ2122222-2-2-2-2222-2-2222-2-2-2-2-2-2-222-20000220000000000000000000022-2-2000000
χ2222222-2-2-2-2222-2-2222-2-2-2-2-2-2-222-200002200000000000000000000-2-222000000
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-10000000000
χ272222-122-2-2-1-1-12-2-22-2-1-1-1-11111112i2i−2i−2i1-1−i−i−i−iiiii00−i3i300−i3i33−33−30000000000
χ282222-122-2-2-1-1-12-2-22-2-1-1-1-11111112i2i−2i−2i1-1−i−i−i−iiiii00i3−i300i3−i3−33−330000000000
χ292222-122-2-2-1-1-12-2-22-2-1-1-1-1111111−2i−2i2i2i1-1iiii−i−i−i−i00−i3i300−i3i3−33−330000000000
χ302222-122-2-2-1-1-12-2-22-2-1-1-1-1111111−2i−2i2i2i1-1iiii−i−i−i−i00i3−i300i3−i33−33−30000000000
χ312222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i32-2-1-10011−i3i3i3−i30000000000
χ322222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-221100-1-1i3−i3−i3i30000000000
χ332222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i32-2-1-10011i3−i3−i3i30000000000
χ342222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-221100-1-1−i3i3i3−i30000000000
χ352222-1-2-2-2-2-1-1-122-2-22-1-111-1-111110000-1133−3−3−3−33300−i3i32i−2ii3−i3−i−iii0000000000
χ362222-1-2-2-2-2-1-1-122-2-22-1-111-1-111110000-1133−3−3−3−33300i3−i3−2i2i−i3i3ii−i−i0000000000
χ372222-1-2-2-2-2-1-1-122-2-22-1-111-1-111110000-11−3−33333−3−300−i3i3−2i2ii3−i3ii−i−i0000000000
χ382222-1-2-2-2-2-1-1-122-2-22-1-111-1-111110000-11−3−33333−3−300i3−i32i−2i−i3i3−i−iii0000000000
χ394444-24444-2-2-2-4-4-4-4422-2-222-222-20000-22000000000000000000000000000000
χ404444-244-4-4-2-2-2-444-4-422-2-2-2-22-2-22000022000000000000000000000000000000
χ414444-2-4-444-2-2-2-44-44-42222-2-2-222-200002-2000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2-4-44442222222-2-220000-2-2000000000000000000000000000000
χ434-44-444i−4i004-4-400000004i−4i000000000000000000000000000000002-22i−2i000000
χ444-44-444i−4i004-4-400000004i−4i00000000000000000000000000000000-22−2i2i000000
χ454-44-44−4i4i004-4-40000000−4i4i000000000000000000000000000000002-2−2i2i000000
χ464-44-44−4i4i004-4-40000000−4i4i00000000000000000000000000000000-222i−2i000000
χ474-4-444004-4-4-4400000000000400-42i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ484-4-444004-4-4-4400000000000400-4−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ494-4-44400-44-4-4400000000000-40042-2-22002-22-2-22-220000000000000000000000
χ504-4-44400-44-4-4400000000000-4004-222-200-22-222-22-20000000000000000000000
χ514-4-44-2004-422-200000−2i32i30000-2−2i32i322i−2i2i−2i002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ524-4-44-2004-422-200000−2i32i30000-2−2i32i32−2i2i−2i2i00−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ534-4-44-2004-422-2000002i3−2i30000-22i3−2i322i−2i2i−2i002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ544-4-44-2004-422-2000002i3−2i30000-22i3−2i32−2i2i−2i2i00−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ554-4-44-200-4422-200000−2i32i3000022i3−2i3-22-2-2200−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ564-4-44-200-4422-200000−2i32i3000022i3−2i3-2-222-2001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000
χ574-4-44-200-4422-2000002i3−2i300002−2i32i3-22-2-2200−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ584-4-44-200-4422-2000002i3−2i300002−2i32i3-2-222-2001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000
χ5988-8-880000-88-8000000000000000000000000000000000000000000000000000
χ6088-8-8-400004-4400000000043−430000000000000000000000000000000000000000
χ6188-8-8-400004-44000000000−43430000000000000000000000000000000000000000
χ628-88-8-48i−8i00-4440000000−4i4i000000000000000000000000000000000000000000
χ638-88-8-4−8i8i00-44400000004i−4i000000000000000000000000000000000000000000

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