Finite Group Databasebeta

← Group #10699166

Character table — Group #10699166

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12223444466624444661212121212121212888812122424242424242424448812121212242424248888448888
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
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ9222222222222-2-2-2-22-2-2222-2-2-2-2200002-2000000000000000000000000002-200
χ10222222222222-2-2-2-22-2-2222-2-2-2-2200002-200000000000000000000000000-2200
χ112222222-2-22222-2-22-222-222-2-2-2-2-22i2i−2i−2i-222i2i2i2i−2i−2i−2i−2i0000000000000000000000
χ122222222-2-22222-2-22-222-222-2-2-2-2-2−2i−2i2i2i-22−2i−2i−2i−2i2i2i2i2i0000000000000000000000
χ132222222-2-2222-222-2-2-2-2-2222222-20000-2-200000000000000000000000000002i−2i
χ142222222-2-2222-222-2-2-2-2-2222222-20000-2-20000000000000000000000000000−2i2i
χ1522222-2-2222222-22-2-2222-2-2-2-22220000-2-2000000002-20022-2-200000000000000
χ1622222-2-2222222-22-2-2222-2-2-2-22220000-2-200000000-2200-2-22200000000000000
χ1722222-2-222222-22-22-2-2-22-2-222-2-220000-220000000000000000000000002-20000
χ1822222-2-222222-22-22-2-2-22-2-222-2-220000-22000000000000000000000000-220000
χ1922222-2-2-2-222222-2-2222-2-2-222-2-2-200002-200000000002i−2i00002i2i−2i−2i0000000000
χ2022222-2-2-2-222222-2-2222-2-2-222-2-2-200002-20000000000−2i2i0000−2i−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
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ272222-122-2-2-1-1-12-2-22-2-1-11-1-1111112i2i−2i−2i1-1−i−i−i−iiiii0000−i3i3−i3i33−33−30000000000
χ282222-122-2-2-1-1-12-2-22-2-1-11-1-1111112i2i−2i−2i1-1−i−i−i−iiiii0000i3−i3i3−i3−33−330000000000
χ292222-122-2-2-1-1-12-2-22-2-1-11-1-111111−2i−2i2i2i1-1iiii−i−i−i−i0000−i3i3−i3i3−33−330000000000
χ302222-122-2-2-1-1-12-2-22-2-1-11-1-111111−2i−2i2i2i1-1iiii−i−i−i−i0000i3−i3i3−i33−33−30000000000
χ312222-1-2-222-1-1-12-22-2-2-1-1-11111-1-1-1000011−i3−i3i3i3−i3−i3i3i32-200-1-111−i3i3i3−i30000000000
χ322222-1-2-222-1-1-12-22-2-2-1-1-11111-1-1-1000011−i3−i3i3i3−i3−i3i3i3-220011-1-1i3−i3−i3i30000000000
χ332222-1-2-222-1-1-12-22-2-2-1-1-11111-1-1-1000011i3i3−i3−i3i3i3−i3−i32-200-1-111i3−i3−i3i30000000000
χ342222-1-2-222-1-1-12-22-2-2-1-1-11111-1-1-1000011i3i3−i3−i3i3i3−i3−i3-220011-1-1−i3i3i3−i30000000000
χ352222-1-2-2-2-2-1-1-122-2-22-1-1111-1-11110000-1133−3−3−3−333002i−2i−i3i3i3−i3−i−iii0000000000
χ362222-1-2-2-2-2-1-1-122-2-22-1-1111-1-11110000-1133−3−3−3−33300−2i2ii3−i3−i3i3ii−i−i0000000000
χ372222-1-2-2-2-2-1-1-122-2-22-1-1111-1-11110000-11−3−33333−3−3002i−2ii3−i3−i3i3−i−iii0000000000
χ382222-1-2-2-2-2-1-1-122-2-22-1-1111-1-11110000-11−3−33333−3−300−2i2i−i3i3i3−i3ii−i−i0000000000
χ394444-24444-2-2-2-4-4-4-4422-2-2-22222-20000-22000000000000000000000000000000
χ404444-244-4-4-2-2-2-444-4-4222-2-2-2-2-2-22000022000000000000000000000000000000
χ414444-2-4-444-2-2-2-44-44-422-222-2-222-200002-2000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2-4-44442222222-2-220000-2-2000000000000000000000000000000
χ434-44-44004-44-4-400000004000000-42-22-2002-22-22-22-20000000000000000000000
χ444-44-44004-44-4-400000004000000-4-22-2200-22-22-22-220000000000000000000000
χ454-44-4400-444-4-40000000-400000042i−2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ464-44-4400-444-4-40000000-40000004−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ474-44-4-2004-4-22200000−2i32i3-20000−2i32i322-22-200−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000
χ484-44-4-2004-4-22200000−2i32i3-20000−2i32i32-22-22001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000
χ494-44-4-2004-4-222000002i3−2i3-200002i3−2i322-22-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000
χ504-44-4-2004-4-222000002i3−2i3-200002i3−2i32-22-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000
χ514-44-4-200-44-22200000−2i32i3200002i3−2i3-22i−2i−2i2i002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ524-44-4-200-44-22200000−2i32i3200002i3−2i3-2−2i2i2i−2i00−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ534-44-4-200-44-222000002i3−2i320000−2i32i3-22i−2i−2i2i002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ544-44-4-200-44-222000002i3−2i320000−2i32i3-2−2i2i2i−2i00−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ554-4-4444i−4i00-44-4000000004i−4i00000000000000000000000000000002-22i−2i000000
χ564-4-4444i−4i00-44-4000000004i−4i0000000000000000000000000000000-22−2i2i000000
χ574-4-444−4i4i00-44-400000000−4i4i00000000000000000000000000000002-2−2i2i000000
χ584-4-444−4i4i00-44-400000000−4i4i0000000000000000000000000000000-222i−2i000000
χ5988-8-880000-8-88000000000000000000000000000000000000000000000000000
χ6088-8-8-4000044-4000000000043−43000000000000000000000000000000000000000
χ6188-8-8-4000044-40000000000−4343000000000000000000000000000000000000000
χ628-8-88-48i−8i004-4400000000−4i4i00000000000000000000000000000000000000000
χ638-8-88-4−8i8i004-44000000004i−4i00000000000000000000000000000000000000000

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