Finite Group Databasebeta

← Group #10695567

Character table — Group #10695567

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122222223446662444666666121212122244666612121212121288882424242424242424444444442444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ9222222222-2-22222-2-2-2222222-2-2-2-222-2-22222-2-2-2-2-2-2000000000000000000000000
χ10222222222-2-22222-2-2-2222222-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ1122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1322222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-11111000000000000
χ1422222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-1000000000000
χ1522222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-1111122-2-2-1-1-1-1111111000033−3−333−3−3000000000000
χ1622222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-1111122-2-2-1-1-1-11111110000−3−333−3−333000000000000
χ1722222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-11111-2-222111111-1-1-1-1000033−3−3−3−333000000000000
χ1822222222-1-2-2-1-1-12-2-2-2-1-1-1-1-1-11111-2-222111111-1-1-1-10000−3−33333−3−3000000000000
χ19222222-2-2222222-22-2-222-2-2-2-222-2-2000000002-2000000000000000000000000002-2
χ20222222-2-2222222-22-2-222-2-2-2-222-2-2000000002-200000000000000000000000000-22
χ21222222-2-22-2-2222-2-22222-2-2-2-2-2-22200000000-22000000000000000022-2-200000000
χ22222222-2-22-2-2222-2-22222-2-2-2-2-2-22200000000-220000000000000000-2-22200000000
χ232222-2-222222222-2-22-2-2-222-2-222-2-200000000-220000000000000000000022-2-20000
χ242222-2-222222222-2-22-2-2-222-2-222-2-200000000-2200000000000000000000-2-2220000
χ252222-2-2222-2-2222-22-22-2-222-2-2-2-222000000002-20000000000000000000000002-200
χ262222-2-2222-2-2222-22-22-2-222-2-2-2-222000000002-2000000000000000000000000-2200
χ272222-2-2-2-22222222-2-22-2-2-2-222222200000000-2-20000002-200002-22-2000000000000
χ282222-2-2-2-22222222-2-22-2-2-2-222222200000000-2-2000000-220000-22-22000000000000
χ292222-2-2-2-22-2-2222222-2-2-2-2-222-2-2-2-2000000002200002i−2i002i−2i2i−2i0000000000000000
χ302222-2-2-2-22-2-2222222-2-2-2-2-222-2-2-2-200000000220000−2i2i00−2i2i−2i2i0000000000000000
χ312222-2-2-2-2-122-1-1-12-2-221111-1-1-1-1-1-10000−i3−i3i3i311−i3−i3i3i3002-2−i3i3i3−i3-11-11000000000000
χ322222-2-2-2-2-122-1-1-12-2-221111-1-1-1-1-1-10000−i3−i3i3i311−i3−i3i3i300-22i3−i3−i3i31-11-1000000000000
χ332222-2-2-2-2-122-1-1-12-2-221111-1-1-1-1-1-10000i3i3−i3−i311i3i3−i3−i3002-2i3−i3−i3i3-11-11000000000000
χ342222-2-2-2-2-122-1-1-12-2-221111-1-1-1-1-1-10000i3i3−i3−i311i3i3−i3−i300-22−i3i3i3−i31-11-1000000000000
χ352222-2-2-2-2-1-2-2-1-1-1222-21111-1-111110000−i3−i3i3i3-1-1i3i3−i3−i32i−2i00−ii−ii3−3−33000000000000
χ362222-2-2-2-2-1-2-2-1-1-1222-21111-1-111110000−i3−i3i3i3-1-1i3i3−i3−i3−2i2i00i−ii−i−333−3000000000000
χ372222-2-2-2-2-1-2-2-1-1-1222-21111-1-111110000i3i3−i3−i3-1-1−i3−i3i3i32i−2i00−ii−ii−333−3000000000000
χ382222-2-2-2-2-1-2-2-1-1-1222-21111-1-111110000i3i3−i3−i3-1-1−i3−i3i3i3−2i2i00i−ii−i3−3−33000000000000
χ39444444-4-4-244-2-2-2-44-4-4-2-22222-2-22200000000-220000000000000000000000000000
χ40444444-4-4-2-4-4-2-2-2-4-444-2-2222222-2-2000000002-20000000000000000000000000000
χ414444-4-444-244-2-2-2-4-44-422-2-222-2-222000000002-20000000000000000000000000000
χ424444-4-444-2-4-4-2-2-2-44-4422-2-22222-2-200000000-220000000000000000000000000000
χ4344-4-4004-4400-44-40000004-4000000000000000000000000000000002i−2i2i−2i00000000
χ4444-4-4004-4400-44-40000004-400000000000000000000000000000000−2i2i−2i2i00000000
χ4544-4-400-44400-44-4000000-44000000000000000000000000000000002i−2i−2i2i00000000
χ4644-4-400-44400-44-4000000-4400000000000000000000000000000000−2i2i2i−2i00000000
χ474-44-4000044i−4i4-4-400000000004i−4i002-22i−2i2-22-2002i−2i2i−2i000000000000000000000000
χ484-44-4000044i−4i4-4-400000000004i−4i00-22−2i2i-22-2200−2i2i−2i2i000000000000000000000000
χ494-44-400004−4i4i4-4-40000000000−4i4i002-2−2i2i2-22-200−2i2i−2i2i000000000000000000000000
χ504-44-400004−4i4i4-4-40000000000−4i4i00-222i−2i-22-22002i−2i2i−2i000000000000000000000000
χ514-44-40000-24i−4i-22200000000−2i32i3−2i2i23−232-22i−2i−1−i31+i3−1+i31−i3002ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ524-44-40000-24i−4i-22200000000−2i32i3−2i2i23−23-22−2i2i1+i3−1−i31−i3−1+i300−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ534-44-40000-24i−4i-222000000002i3−2i3−2i2i−23232-22i−2i−1+i31−i3−1−i31+i3002ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ544-44-40000-24i−4i-222000000002i3−2i3−2i2i−2323-22−2i2i1−i3−1+i31+i3−1−i300−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ554-44-40000-2−4i4i-22200000000−2i32i32i−2i−23232-2−2i2i−1−i31+i3−1+i31−i300−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ564-44-40000-2−4i4i-22200000000−2i32i32i−2i−2323-222i−2i1+i3−1−i31−i3−1+i3002ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ574-44-40000-2−4i4i-222000000002i3−2i32i−2i23−232-2−2i2i−1+i31−i3−1−i31+i300−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ584-44-40000-2−4i4i-222000000002i3−2i32i−2i23−23-222i−2i1−i3−1+i31+i3−1−i3002ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ594-4-444-400400-4-4400004-4000000000000000000000000000000000000002-22-20000
χ604-4-444-400400-4-4400004-400000000000000000000000000000000000000-22-220000
χ614-4-44-4400400-4-440000-44000000000000000000000000000000000000002-2-220000
χ624-4-44-4400400-4-440000-4400000000000000000000000000000000000000-222-20000
χ6388-8-8008-8-4004-44000000-4400000000000000000000000000000000000000000000
χ6488-8-800-88-4004-440000004-400000000000000000000000000000000000000000000
χ658-8-888-800-40044-40000-440000000000000000000000000000000000000000000000
χ668-8-88-8800-40044-400004-40000000000000000000000000000000000000000000000

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