Finite Group Databasebeta

← Group #69796

Character table — Group #69796

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222244444444444444444121212122424111122222222222244444444444444444121212122424
order12223444466612121212488881212121224242424242424248888242222644446661212121248888121212122424242424242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ511111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-111111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1
χ611111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-1111111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11
χ711111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-1111111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11
χ811111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-111111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1
χ92222222-2-22222222-20000-2-2-2-2000000000000002222222-2-22222222-20000-2-2-2-200000000000000
χ1022222-2-222222-2-2-2-2-20000-2-2220000000000000022222-2-222222-2-2-2-2-20000-2-22200000000000000
χ112222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-10000002222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000
χ122222-12222-1-1-1-1-1-1-12-2-2-2-2-1-1-1-1111111110000002222-12222-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000
χ132222-122-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i30000002222-122-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000
χ142222-122-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i30000002222-122-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000
χ152222-1-2-222-1-1-11111-2000011-1-133−3−3−3−3330000002222-1-2-222-1-1-11111-2000011-1-133−3−3−3−333000000
χ162222-1-2-222-1-1-11111-2000011-1-1−3−33333−3−30000002222-1-2-222-1-1-11111-2000011-1-1−3−33333−3−3000000
χ172222-1-2-2-2-2-1-1-1111122i2i−2i−2i-1-111−i−i−i−iiiii0000002222-1-2-2-2-2-1-1-1111122i2i−2i−2i-1-111−i−i−i−iiiii000000
χ182222-1-2-2-2-2-1-1-111112−2i−2i2i2i-1-111iiii−i−i−i−i0000002222-1-2-2-2-2-1-1-111112−2i−2i2i2i-1-111iiii−i−i−i−i000000
χ1922-2-22002i−2i2-2-2000001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000022-2-22002i−2i2-2-2000001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2022-2-22002i−2i2-2-200000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000022-2-22002i−2i2-2-200000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2122-2-2200−2i2i2-2-2000001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000022-2-2200−2i2i2-2-2000001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2222-2-2200−2i2i2-2-200000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000022-2-2200−2i2i2-2-200000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2322-2-2-1002i−2i-111−i3−i3i3i301+i−1−i1−i−1+i3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000022-2-2-1002i−2i-111−i3−i3i3i301+i−1−i1−i−1+i3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000
χ2422-2-2-1002i−2i-111−i3−i3i3i30−1−i1+i−1+i1−i3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000022-2-2-1002i−2i-111−i3−i3i3i30−1−i1+i−1+i1−i3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000
χ2522-2-2-1002i−2i-111i3i3−i3−i301+i−1−i1−i−1+i−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000022-2-2-1002i−2i-111i3i3−i3−i301+i−1−i1−i−1+i−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000
χ2622-2-2-1002i−2i-111i3i3−i3−i30−1−i1+i−1+i1−i−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000022-2-2-1002i−2i-111i3i3−i3−i30−1−i1+i−1+i1−i−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000
χ2722-2-2-100−2i2i-111−i3−i3i3i301−i−1+i1+i−1−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000022-2-2-100−2i2i-111−i3−i3i3i301−i−1+i1+i−1−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000
χ2822-2-2-100−2i2i-111−i3−i3i3i30−1+i1−i−1−i1+i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000022-2-2-100−2i2i-111−i3−i3i3i30−1+i1−i−1−i1+i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000
χ2922-2-2-100−2i2i-111i3i3−i3−i301−i−1+i1+i−1−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000022-2-2-100−2i2i-111i3i3−i3−i301−i−1+i1+i−1−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000
χ3022-2-2-100−2i2i-111i3i3−i3−i30−1+i1−i−1−i1+i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000022-2-2-100−2i2i-111i3i3−i3−i30−1+i1−i−1−i1+i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000
χ312-22-222i−2i00-22-22i−2i2i−2i000000000000000001+i−1−i1−i−1+i002-22-222i−2i00-22-22i−2i2i−2i000000000000000001+i−1−i1−i−1+i00
χ322-22-222i−2i00-22-22i−2i2i−2i00000000000000000−1−i1+i−1+i1−i002-22-222i−2i00-22-22i−2i2i−2i00000000000000000−1−i1+i−1+i1−i00
χ332-22-22−2i2i00-22-2−2i2i−2i2i000000000000000001−i−1+i1+i−1−i002-22-22−2i2i00-22-2−2i2i−2i2i000000000000000001−i−1+i1+i−1−i00
χ342-22-22−2i2i00-22-2−2i2i−2i2i00000000000000000−1+i1−i−1−i1+i002-22-22−2i2i00-22-2−2i2i−2i2i00000000000000000−1+i1−i−1−i1+i00
χ354-44-4-24i−4i002-22−2i2i−2i2i000000000000000000000004-44-4-24i−4i002-22−2i2i−2i2i00000000000000000000000
χ364-44-4-2−4i4i002-222i−2i2i−2i000000000000000000000004-44-4-2−4i4i002-222i−2i2i−2i00000000000000000000000
χ374-4-4440000-4-440000000000000000000000000004-4-4440000-4-44000000000000000000000000000
χ384-4-44-2000022-223−23−2323000000000000000000000004-4-44-2000022-223−23−232300000000000000000000000
χ394-4-44-2000022-2−232323−23000000000000000000000004-4-44-2000022-2−232323−2300000000000000000000000
χ40111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ4211111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ4311111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ4411111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1-1-1-1-1-11111-1-1-11111-1−i−iii-1-111−i−i−i−iiiii−i−iii-11
χ4511111-1-1-1-1111-1-1-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11-1-1-1-1-11111-1-1-11111-1−i−iii-1-111−i−i−i−iiiiiii−i−i1-1
χ4611111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11-1-1-1-1-11111-1-1-11111-1ii−i−i-1-111iiii−i−i−i−i−i−iii1-1
χ4711111-1-1-1-1111-1-1-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1-1-1-1-1-11111-1-1-11111-1ii−i−i-1-111iiii−i−i−i−iii−i−i-11
χ482222222-2-22222222-20000-2-2-2-200000000000000-2-2-2-2-2-2-222-2-2-2-2-2-2-220000222200000000000000
χ4922222-2-222222-2-2-2-2-20000-2-22200000000000000-2-2-2-2-222-2-2-2-2-222222000022-2-200000000000000
χ502222-12222-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-21-2-2-2-21111111-2-2-2-2-2111111111111000000
χ512222-12222-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000-2-2-2-21-2-2-2-21111111-222221111-1-1-1-1-1-1-1-1000000
χ522222-122-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000-2-2-2-21-2-222111111120000-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000
χ532222-122-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000-2-2-2-21-2-222111111120000-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000
χ542222-1-2-222-1-1-11111-2000011-1-133−3−3−3−333000000-2-2-2-2122-2-2111-1-1-1-120000-1-111−3−33333−3−3000000
χ552222-1-2-222-1-1-11111-2000011-1-1−3−33333−3−3000000-2-2-2-2122-2-2111-1-1-1-120000-1-11133−3−3−3−333000000
χ562222-1-2-2-2-2-1-1-1111122i2i−2i−2i-1-111−i−i−i−iiiii000000-2-2-2-212222111-1-1-1-1-2−2i−2i2i2i11-1-1iiii−i−i−i−i000000
χ572222-1-2-2-2-2-1-1-111112−2i−2i2i2i-1-111iiii−i−i−i−i000000-2-2-2-212222111-1-1-1-1-22i2i−2i−2i11-1-1−i−i−i−iiiii000000
χ5822-2-22002i−2i2-2-2000001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000-2-222-200−2i2i-22200000−1−i1+i−1+i1−i00−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ5922-2-22002i−2i2-2-200000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000-2-222-200−2i2i-222000001+i−1−i1−i−1+i00−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ6022-2-2200−2i2i2-2-2000001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000-2-222-2002i−2i-22200000−1+i1−i−1−i1+i002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ6122-2-2200−2i2i2-2-200000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000-2-222-2002i−2i-222000001−i−1+i1+i−1−i002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ6222-2-2-1002i−2i-111−i3−i3i3i301+i−1−i1−i−1+i3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000-2-222100−2i2i1-1-1i3i3−i3−i30−1−i1+i−1+i1−i−33i−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000
χ6322-2-2-1002i−2i-111−i3−i3i3i30−1−i1+i−1+i1−i3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000-2-222100−2i2i1-1-1i3i3−i3−i301+i−1−i1−i−1+i−33i−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000
χ6422-2-2-1002i−2i-111i3i3−i3−i301+i−1−i1−i−1+i−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000-2-222100−2i2i1-1-1−i3−i3i3i30−1−i1+i−1+i1−i3−3i−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000
χ6522-2-2-1002i−2i-111i3i3−i3−i30−1−i1+i−1+i1−i−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000-2-222100−2i2i1-1-1−i3−i3i3i301+i−1−i1−i−1+i3−3i−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000
χ6622-2-2-100−2i2i-111−i3−i3i3i301−i−1+i1+i−1−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000-2-2221002i−2i1-1-1i3i3−i3−i30−1+i1−i−1−i1+i3−3−iiζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000
χ6722-2-2-100−2i2i-111−i3−i3i3i30−1+i1−i−1−i1+i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000-2-2221002i−2i1-1-1i3i3−i3−i301−i−1+i1+i−1−i3−3−ii−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000
χ6822-2-2-100−2i2i-111i3i3−i3−i301−i−1+i1+i−1−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000-2-2221002i−2i1-1-1−i3−i3i3i30−1+i1−i−1−i1+i−33−iiζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000
χ6922-2-2-100−2i2i-111i3i3−i3−i30−1+i1−i−1−i1+i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000-2-2221002i−2i1-1-1−i3−i3i3i301−i−1+i1+i−1−i−33−ii−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000
χ702-22-222i−2i00-22-22i−2i2i−2i000000000000000001+i−1−i1−i−1+i00-22-22-2−2i2i002-22−2i2i−2i2i00000000000000000−1−i1+i−1+i1−i00
χ712-22-222i−2i00-22-22i−2i2i−2i00000000000000000−1−i1+i−1+i1−i00-22-22-2−2i2i002-22−2i2i−2i2i000000000000000001+i−1−i1−i−1+i00
χ722-22-22−2i2i00-22-2−2i2i−2i2i000000000000000001−i−1+i1+i−1−i00-22-22-22i−2i002-222i−2i2i−2i00000000000000000−1+i1−i−1−i1+i00
χ732-22-22−2i2i00-22-2−2i2i−2i2i00000000000000000−1+i1−i−1−i1+i00-22-22-22i−2i002-222i−2i2i−2i000000000000000001−i−1+i1+i−1−i00
χ744-44-4-24i−4i002-22−2i2i−2i2i00000000000000000000000-44-442−4i4i00-22-22i−2i2i−2i00000000000000000000000
χ754-44-4-2−4i4i002-222i−2i2i−2i00000000000000000000000-44-4424i−4i00-22-2−2i2i−2i2i00000000000000000000000
χ764-4-4440000-4-44000000000000000000000000000-444-4-4000044-4000000000000000000000000000
χ774-4-44-2000022-223−23−232300000000000000000000000-444-420000-2-22−232323−2300000000000000000000000
χ784-4-44-2000022-2−232323−2300000000000000000000000-444-420000-2-2223−23−232300000000000000000000000

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