Finite Group Databasebeta

← Group #10698434

Character table — Group #10698434

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order1222223444466622446666661212121244441212121212121212121244441212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2222-2-22-2-2-222-2-222-2-200002-200000000000000000000000022-2-20000
χ10222222222-2-2222-2-22-2-2-222-2-222-2-200002-2000000000000000000000000-2-2220000
χ112222222-2-222222-2-2-22-2-222-2-2-2-2220000-220000000000000000000022-2-200000000
χ122222222-2-222222-2-2-22-2-222-2-2-2-2220000-2200000000000000000000-2-22200000000
χ132222222-2-2-2-222222-2-2222222-2-2-2-20000-2-2000000002-20022-2-20000000000000000
χ142222222-2-2-2-222222-2-2222222-2-2-2-20000-2-200000000-2200-2-2220000000000000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-11111000011−i3−i3−i3−i3i3i3i3i32-200-1-111−i3−i3i3i3000000000000
χ20222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-11111000011−i3−i3−i3−i3i3i3i3i3-220011-1-1i3i3−i3−i3000000000000
χ21222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-11111000011i3i3i3i3−i3−i3−i3−i32-200-1-111i3i3−i3−i3000000000000
χ22222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-11111000011i3i3i3i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i3000000000000
χ232222-2-2222222222-2-2-222-2-2-2-222220000-2-200000000002i−2i00002i−2i2i−2i000000000000
χ242222-2-2222222222-2-2-222-2-2-2-222220000-2-20000000000−2i2i0000−2i2i−2i2i000000000000
χ252222-2-2222-2-2222-22-22-2-2-2-22222-2-20000-2200000000000000000000000000002i−2i00
χ262222-2-2222-2-2222-22-22-2-2-2-22222-2-20000-220000000000000000000000000000−2i2i00
χ272222-2-22-2-222222-222-2-2-2-2-222-2-22200002-20000000000000000000000000000002i−2i
χ282222-2-22-2-222222-222-2-2-2-2-222-2-22200002-2000000000000000000000000000000−2i2i
χ292222-2-22-2-2-2-22222-22222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2000000000000000000000000
χ302222-2-22-2-2-2-22222-22222-2-2-2-2-2-2-2-2-2-22222-2-222-2-222000000000000000000000000
χ312222-2-2-12222-1-1-12-2-2-2-1-11111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i3002i−2i3−33−3−ii−ii000000000000
χ322222-2-2-12222-1-1-12-2-2-2-1-11111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i300−2i2i−33−33i−ii−i000000000000
χ332222-2-2-12222-1-1-12-2-2-2-1-11111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i3002i−2i−33−33−ii−ii000000000000
χ342222-2-2-12222-1-1-12-2-2-2-1-11111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i300−2i2i3−33−3i−ii−i000000000000
χ352222-2-2-1-2-2-2-2-1-1-12-222-1-11111111122-2-2-1-1-1-111-1-11100003−3−333−3−33000000000000
χ362222-2-2-1-2-2-2-2-1-1-12-222-1-11111111122-2-2-1-1-1-111-1-1110000−333−3−333−3000000000000
χ372222-2-2-1-2-2-2-2-1-1-12-222-1-111111111-2-222-1-111-1-111-1-100003−3−33−333−3000000000000
χ382222-2-2-1-2-2-2-2-1-1-12-222-1-111111111-2-222-1-111-1-111-1-10000−333−33−3−33000000000000
χ39444444-244-4-4-2-2-2-4-44-422-2-222-2-2220000-2200000000000000000000000000000000
χ40444444-2-4-444-2-2-2-4-4-4422-2-22222-2-200002-200000000000000000000000000000000
χ414444-4-4-244-4-4-2-2-2-44-442222-2-2-2-22200002-200000000000000000000000000000000
χ424444-4-4-2-4-444-2-2-2-444-42222-2-222-2-20000-2200000000000000000000000000000000
χ4344-4-4004004i−4i4-4-40000000000004i−4i0000000000000000000000000000002-22i−2i0000
χ4444-4-4004004i−4i4-4-40000000000004i−4i000000000000000000000000000000-22−2i2i0000
χ4544-4-400400−4i4i4-4-4000000000000−4i4i0000000000000000000000000000002-2−2i2i0000
χ4644-4-400400−4i4i4-4-4000000000000−4i4i000000000000000000000000000000-222i−2i0000
χ474-44-40044i−4i00-44-400000000004i−4i00000000000000000000000000002-22i−2i00000000
χ484-44-40044i−4i00-44-400000000004i−4i0000000000000000000000000000-22−2i2i00000000
χ494-44-4004−4i4i00-44-40000000000−4i4i00000000000000000000000000002-2−2i2i00000000
χ504-44-4004−4i4i00-44-40000000000−4i4i0000000000000000000000000000-222i−2i00000000
χ514-4-444-440000-4-440000004-40000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ524-4-444-440000-4-440000004-4000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ534-4-444-4-2000022-20000−2i32i3-22−2i32i300002i−2i2i−2i002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11000000000000000000000000
χ544-4-444-4-2000022-20000−2i32i3-22−2i32i30000−2i2i−2i2i00−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ11000000000000000000000000
χ554-4-444-4-2000022-200002i3−2i3-222i3−2i300002i−2i2i−2i002ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ7000000000000000000000000
χ564-4-444-4-2000022-200002i3−2i3-222i3−2i30000−2i2i−2i2i00−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ7000000000000000000000000
χ574-4-44-4440000-4-44000000-440000002i−2i−2i2i002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ584-4-44-4440000-4-44000000-44000000−2i2i2i−2i00−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ594-4-44-44-2000022-20000−2i32i32-22i3−2i300002i−2i−2i2i002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11000000000000000000000000
χ604-4-44-44-2000022-20000−2i32i32-22i3−2i30000−2i2i2i−2i00−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11000000000000000000000000
χ614-4-44-44-2000022-200002i3−2i32-2−2i32i300002i−2i−2i2i002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ624-4-44-44-2000022-200002i3−2i32-2−2i32i30000−2i2i2i−2i00−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ6388-8-800-4008i−8i-444000000000000−4i4i00000000000000000000000000000000000000
χ6488-8-800-400−8i8i-4440000000000004i−4i00000000000000000000000000000000000000
χ658-88-800-48i−8i004-440000000000−4i4i0000000000000000000000000000000000000000
χ668-88-800-4−8i8i004-4400000000004i−4i0000000000000000000000000000000000000000

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