Finite Group Databasebeta

← Group #13155612

Character table — Group #13155612

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size11112222222222222222224444444444444444444444446666666666666666666666668888888888999912121212121212121212121212121212121212121212121212121818181818181818181824242424242424243636363672727272108108
order122233344666666666121212123336666666661212121212121212121212128888888824242424242424242424242424242424366612121212121244442224242424242424242424242424242424242424242424242444121212121212121266666666224466121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1
χ911-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-111-111-1-1ii−i−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−iiiii−i−i−i−i1-11-111-1-11-1i−i1-1i−ii−i
χ1011-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1-111-111-1-1ii−i−i-11111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−iiiii−i−i−i−i-11-11-1-111-11−ii-11−ii−ii
χ1111-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-111-111-1-1−i−iii1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−i−i−iiiii1-11-111-1-11-1−ii1-1−ii−ii
χ1211-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1-111-111-1-1−i−iii-11111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−i−i−i−iiiii-11-11-1-111-11i−i-11i−ii−i
χ1311-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-111-111-1-1−i−iii1-1-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−i−i−i−iiiii1-11-111-1-1-11i−i-11i−i−ii
χ1411-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-111-111-1-1−i−iii-11-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−i−i−i−iiiii-11-11-1-1111-1−ii1-1−iii−i
χ1511-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-111-111-1-1ii−i−i1-1-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−iiiii−i−i−i−i1-11-111-1-1-11−ii-11−iii−i
χ1611-1-11111-1-1-1-1111-1-1-111-1-1111-1-1-1-1-1-11111-111-1-11-111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-111-111-1-1ii−i−i-11-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−iiiii−i−i−i−i-11-11-1-1111-1i−i1-1i−i−ii
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2222200000000000000000000000000-2-222-2-222-2-2000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2-2-2-2-20000000000000000000000000022-2-222-2-222000000000000000000
χ19222222-1222-1-122-122222222-1-122-1-1-1-12-1-12-122-1-1-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000022-1-1-1-1-1-12200-1-10000
χ20222222-1222-1-122-122222222-1-122-1-1-1-12-1-12-122-1-1-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-10000-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000-2-2111111-2-200110000
χ21222222-1222-1-122-122222222-1-122-1-1-1-12-1-12-122-1-1-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1000022111111111111000000000000000000000022-1-1-1-1-1-1-2-200110000
χ22222222-1222-1-122-122222222-1-122-1-1-1-12-1-12-122-1-1-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-10000-2-21111111111110000000000000000000000-2-21111112200-1-10000
χ2322222-1222-1222-1222-12222-12-1-1-122-1-1-12-1-12-1-1222-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000022000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-122-1-1-1-1002200-1-100
χ2422222-1222-1222-1222-12222-12-1-1-122-1-1-12-1-12-1-1222-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-10000-2-2000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000011-2-2111100-2-2001100
χ2522222-1222-1222-1222-12222-12-1-1-122-1-1-12-1-12-1-1222-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000220000000000001111111111110000000000-1-122-1-1-1-100-2-2001100
χ2622222-1222-1222-1222-12222-12-1-1-122-1-1-12-1-12-1-1222-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2000000000000111111111111000000000011-2-21111002200-1-100
χ272222-12222222-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122220022-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000
χ282222-12222222-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-1-2-2-2-20022-1-1-1-122-1-1-1-1-2-21111-2-21111-2-211111111000000000000000000
χ292222-12222222-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-200-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-211111111000000000000000000
χ302222-12222222-122-1-12-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1222200-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000000000
χ312222-122-2-2222-122-1-121111-1-12-1-1-1-122-1-12-2-21111-2-211110000000033−3−333−3−333−3−333−3−3-1-1-1-1-2-211112222000033−3−30033−3−30033−3−30033−3−3-2-2-1-111-1-111000000000000000000
χ322222-122-2-2222-122-1-121111-1-12-1-1-1-122-1-12-2-21111-2-211110000000033−3−333−3−3−3−333−3−333-1-1-1-1-2-21111-2-2-2-2000033−3−30033−3−300−3−33300−3−3332211-1-111-1-1000000000000000000
χ332222-122-2-2222-122-1-121111-1-12-1-1-1-122-1-12-2-21111-2-2111100000000−3−333−3−33333−3−333−3−3-1-1-1-1-2-21111-2-2-2-20000−3−33300−3−3330033−3−30033−3−32211-1-111-1-1000000000000000000
χ342222-122-2-2222-122-1-121111-1-12-1-1-1-122-1-12-2-21111-2-2111100000000−3−333−3−333−3−333−3−333-1-1-1-1-2-2111122220000−3−33300−3−33300−3−33300−3−333-2-2-1-111-1-111000000000000000000
χ3522-2-2222-22-2-2-2222-2-2-2-2-222222-2-2-2-2-2-2222-22-2-222-22-2-2220000000000000000000000002-2-22-22-2-2222i2i−2i−2i00000000000000000000000000−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000
χ3622-2-2222-22-2-2-2222-2-2-2-2-222222-2-2-2-2-2-2222-22-2-222-22-2-2220000000000000000000000002-2-22-22-2-222−2i−2i2i2i000000000000000000000000002i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000
χ3722-2-222-12-2-21122-1-2-2-222-2-22-1-1-2-211112-1-1212211-1-2-1-1-2-222-2-200002222-2-2-2-200000000-111-1-11-1-11100002-2-1-1-1-1-1-111111100000000000000000000002-2-11-1-1112-200-110000
χ3822-2-222-12-2-21122-1-2-2-222-2-22-1-1-2-211112-1-1212211-1-2-1-1-2-222-2-200002222-2-2-2-200000000-111-1-11-1-1110000-22-1-1-1-1-1-11111110000000000000000000000-221-111-1-1-22001-10000
χ3922-2-222-12-2-21122-1-2-2-222-2-22-1-1-2-211112-1-1212211-1-2-1-1-2-2-2-2220000-2-2-2-2222200000000-111-1-11-1-11100002-2111111-1-1-1-1-1-100000000000000000000002-2-11-1-111-22001-10000
χ4022-2-222-12-2-21122-1-2-2-222-2-22-1-1-2-211112-1-1212211-1-2-1-1-2-2-2-2220000-2-2-2-2222200000000-111-1-11-1-1110000-22111111-1-1-1-1-1-10000000000000000000000-221-111-1-12-200-110000
χ4122-2-22-122-21-2-22-12-2-2122-2-2-12-111-2-211-12-1-1-2-1-1-2-221221100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-111-1-11-1-11100002-2000000000000−i−i−i−i−i−iiiiiii0000000000-112-2-1-111002i−2i00−ii00
χ4222-2-22-122-21-2-22-12-2-2122-2-2-12-111-2-211-12-1-1-2-1-1-2-221221100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-111-1-11-1-1110000-22000000000000−i−i−i−i−i−iiiiiii00000000001-1-2211-1-100−2i2i00i−i00
χ4322-2-22-122-21-2-22-12-2-2122-2-2-12-111-2-211-12-1-1-2-1-1-2-22122110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-111-1-11-1-11100002-2000000000000iiiiii−i−i−i−i−i−i0000000000-112-2-1-11100−2i2i00i−i00
χ4422-2-22-122-21-2-22-12-2-2122-2-2-12-111-2-211-12-1-1-2-1-1-2-22122110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-111-1-11-1-1110000-22000000000000iiiiii−i−i−i−i−i−i00000000001-1-2211-1-1002i−2i00−ii00
χ4522-2-2-1222-2-2-2-2-12211-2-1-111-1-121111-2-2-1-122-2-1-1112-2-1-11122-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii-111-12-2-1-1112i2i−2i−2i0022-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i−2i−i−i−i−iiiii000000000000000000
χ4622-2-2-1222-2-2-2-2-12211-2-1-111-1-121111-2-2-1-122-2-1-1112-2-1-11122-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i-111-12-2-1-111−2i−2i2i2i0022-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i2iiiii−i−i−i−i000000000000000000
χ4722-2-2-1222-2-2-2-2-12211-2-1-111-1-121111-2-2-1-122-2-1-1112-2-1-111-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii-111-12-2-1-111−2i−2i2i2i00-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i2iiiii−i−i−i−i000000000000000000
χ4822-2-2-1222-2-2-2-2-12211-2-1-111-1-121111-2-2-1-122-2-1-1112-2-1-111-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i-111-12-2-1-1112i2i−2i−2i00-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i−2i−i−i−i−iiiii000000000000000000
χ4922-2-2-122-22-2-2-2-12211-211-1-1-1-121111-2-2-1-12-2211-1-1-2211-1-10000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3-111-1-2211-1-1−2i−2i2i2i000033−3−300−3−33300−i3−i3i3i300i3i3−i3−i32i−2iii−i−i−i−iii000000000000000000
χ5022-2-2-122-22-2-2-2-12211-211-1-1-1-121111-2-2-1-12-2211-1-1-2211-1-10000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3-111-1-2211-1-12i2i−2i−2i000033−3−300−3−33300i3i3−i3−i300−i3−i3i3i3−2i2i−i−iiiii−i−i000000000000000000
χ5122-2-2-122-22-2-2-2-12211-211-1-1-1-121111-2-2-1-12-2211-1-1-2211-1-100000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3-111-1-2211-1-12i2i−2i−2i0000−3−3330033−3−300−i3−i3i3i300i3i3−i3−i3−2i2i−i−iiiii−i−i000000000000000000
χ5222-2-2-122-22-2-2-2-12211-211-1-1-1-121111-2-2-1-12-2211-1-1-2211-1-100000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3-111-1-2211-1-1−2i−2i2i2i0000−3−3330033−3−300i3i3−i3−i300−i3−i3i3i32i−2iii−i−i−i−iii000000000000000000
χ532-22-22220022-2-2-2-22-2-200002222-22-22-2-2-2-20000000000002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i222-2-20000002i−2i2i−2i002−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i00000000000000000000
χ542-22-22220022-2-2-2-22-2-200002222-22-22-2-2-2-20000000000002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i222-2-2000000−2i2i−2i2i002−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i00000000000000000000
χ552-22-22220022-2-2-2-22-2-200002222-22-22-2-2-2-2000000000000−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i222-2-2000000−2i2i−2i2i00−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i00000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.