Finite Group Databasebeta

← Group #13137412

Character table — Group #13137412

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444434444666121212121212121233666666121212121212121212121212121212123666121212121212121212121212121212128888888824242424242424242424242424242424224466668888121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ5111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1
χ6111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111
χ7111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-11111
χ8111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-1−ii−ii1111−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11111−ii−ii-1-1-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-1i−ii−i1111ii−i−iii−i−i
χ131111-1-1-1-11-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1i−i−ii-1-111ii−i−i−i−iii
χ141111-1-1-1-11-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1-1-111−iii−i11-1-1−i−iiiii−i−i
χ151111-1-1-1-11-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1−iii−i-1-111−i−iiiii−i−i
χ161111-1-1-1-11-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-111i−i−ii11-1-1ii−i−i−i−iii
χ172222222222222222222222222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222222222222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ19222222222222222222222222-12-1-1-1222-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000000022220000-1-1-1-1-1-1-1-1
χ20222222222222222222222222-12-1-1-1222-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000-2-2-2-2000011111111
χ21222222222-2-2-2-22222222-2-2-2-22-1222-1-1-12211111111-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ22222222222-2-2-2-22222222-2-2-2-22-1222-1-1-12211111111-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ23222222222-2-2-2-22222222-2-2-2-2-12-1-1-1222-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-11111-1-1-1-1111111110000000000000000000000000000000022-2-20000-1-1-1-11111
χ24222222222-2-2-2-22222222-2-2-2-2-12-1-1-1222-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-11111-1-1-1-11111111100000000000000000000000000000000-2-22200001111-1-1-1-1
χ252222-2-2-2-2222-2-2222-2-2-2-222-2-22-1222-1-1-1-2-2-1-1-1-111111111-2-2-1-1-1-122-2-21111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-222-2-22-1222-1-1-1-2-2-1-1-1-111111111-2-2-1-1-1-122-2-21111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ272222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1222112222-2-2-2-2-2-2-2-211-1-1-1-1-1-1111111-1-1-1-11111000000000000000000000000000000002i−2i2i−2i0000−i−iii−i−iii
χ282222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1222112222-2-2-2-2-2-2-2-211-1-1-1-1-1-1111111-1-1-1-1111100000000000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i
χ292222-2-2-2-22-2-222222-2-2-2-2-2-2222-1222-1-1-1-2-21111-1-1-1-11111-2-2-1-1-1-1-2-22211111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ302222-2-2-2-22-2-222222-2-2-2-2-2-2222-1222-1-1-1-2-21111-1-1-1-11111-2-2-1-1-1-1-2-22211111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ312222-2-2-2-22-2-222222-2-2-2-2-2-222-12-1-1-122211-2-2-2-22222-2-2-2-211-1-1-1-111-1-111111111-1-1-1-1000000000000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i
χ322222-2-2-2-22-2-222222-2-2-2-2-2-222-12-1-1-122211-2-2-2-22222-2-2-2-211-1-1-1-111-1-111111111-1-1-1-100000000000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii
χ3322-2-22i−2i2i−2i200002-2-22i2i−2i−2i0000222-2-22-2-22i−2i000000002i2i−2i−2i2i−2i22-2-200002i2i−2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000
χ3422-2-22i−2i2i−2i200002-2-22i2i−2i−2i0000222-2-22-2-22i−2i000000002i2i−2i−2i2i−2i22-2-200002i2i−2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ3522-2-22i−2i2i−2i200002-2-22i2i−2i−2i00002-12-2-2-1112i−2i33−3−3−i3−i3i3i3−i−iii2i−2i-1-1110000−i−iii33−3−3−i3−i3i3i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000000000000000
χ3622-2-22i−2i2i−2i200002-2-22i2i−2i−2i00002-12-2-2-1112i−2i33−3−3−i3−i3i3i3−i−iii2i−2i-1-1110000−i−iii33−3−3−i3−i3i3i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000000000000000
χ3722-2-22i−2i2i−2i200002-2-22i2i−2i−2i00002-12-2-2-1112i−2i−3−333i3i3−i3−i3−i−iii2i−2i-1-1110000−i−iii−3−333i3i3−i3−i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000000000000000
χ3822-2-22i−2i2i−2i200002-2-22i2i−2i−2i00002-12-2-2-1112i−2i−3−333i3i3−i3−i3−i−iii2i−2i-1-1110000−i−iii−3−333i3i3−i3−i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000000000000000
χ3922-2-2−2i2i−2i2i200002-2-2−2i−2i2i2i0000222-2-22-2-2−2i2i00000000−2i−2i2i2i−2i2i22-2-20000−2i−2i2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ4022-2-2−2i2i−2i2i200002-2-2−2i−2i2i2i0000222-2-22-2-2−2i2i00000000−2i−2i2i2i−2i2i22-2-20000−2i−2i2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000
χ4122-2-2−2i2i−2i2i200002-2-2−2i−2i2i2i00002-12-2-2-111−2i2i33−3−3i3i3−i3−i3ii−i−i−2i2i-1-1110000ii−i−i33−3−3i3i3−i3−i3−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000000000000000
χ4222-2-2−2i2i−2i2i200002-2-2−2i−2i2i2i00002-12-2-2-111−2i2i33−3−3i3i3−i3−i3ii−i−i−2i2i-1-1110000ii−i−i33−3−3i3i3−i3−i32ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000000000000000000000
χ4322-2-2−2i2i−2i2i200002-2-2−2i−2i2i2i00002-12-2-2-111−2i2i−3−333−i3−i3i3i3ii−i−i−2i2i-1-1110000ii−i−i−3−333−i3−i3i3i3−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000000000000000000000
χ4422-2-2−2i2i−2i2i200002-2-2−2i−2i2i2i00002-12-2-2-111−2i2i−3−333−i3−i3i3i3ii−i−i−2i2i-1-1110000ii−i−i−3−333−i3−i3i3i32ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000000000000000
χ452-22-22i−2i−2i2i22-22i−2i-22-22i−2i2i−2i2-22i−2i22-22-2-22-22i−2i2-22-22i−2i2i−2i2i−2i2i−2i−2i2i2-22-22-22i−2i2i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000000000000000000000000000
χ462-22-22i−2i−2i2i22-22i−2i-22-22i−2i2i−2i2-22i−2i2-1-22-21-112i−2i-11-11−ii−ii−ii−ii−2i2i-11-112-22i−2i−ii−ii-11-11−ii−ii00000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ472-22-22i−2i−2i2i22-22i−2i-22-22i−2i2i−2i2-22i−2i2-1-22-21-112i−2i-11-11−ii−ii−ii−ii−2i2i-11-112-22i−2i−ii−ii-11-11−ii−ii00000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ482-22-22i−2i−2i2i22-22i−2i-22-22i−2i2i−2i2-22i−2i-121-11-22-2−ii2-22-22i−2i2i−2i2i−2i2i−2ii−i-11-11-11−ii−ii−ii-11-11−ii−ii0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ492-22-22i−2i−2i2i22-22i−2i-22-22i−2i2i−2i2-22i−2i-121-11-22-2−ii2-22-22i−2i2i−2i2i−2i2i−2ii−i-11-11-11−ii−ii−ii-11-11−ii−ii0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ502-22-22i−2i−2i2i2-22−2i2i-22-22i−2i2i−2i-22−2i2i22-22-2-22-22i−2i-22-22−2i2i−2i2i2i−2i2i−2i−2i2i2-22-2-22−2i2i2i−2i2i−2i-22-22−2i2i−2i2i000000000000000000000000000000000000000000000000
χ512-22-22i−2i−2i2i2-22−2i2i-22-22i−2i2i−2i-22−2i2i2-1-22-21-112i−2i1-11-1i−ii−i−ii−ii−2i2i-11-11-22−2i2i−ii−ii1-11-1i−ii−i00000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ522-22-22i−2i−2i2i2-22−2i2i-22-22i−2i2i−2i-22−2i2i2-1-22-21-112i−2i1-11-1i−ii−i−ii−ii−2i2i-11-11-22−2i2i−ii−ii1-11-1i−ii−i00000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ532-22-22i−2i−2i2i2-22−2i2i-22-22i−2i2i−2i-22−2i2i-121-11-22-2−ii-22-22−2i2i−2i2i2i−2i2i−2ii−i-11-111-1i−i−ii−ii1-11-1i−ii−i0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.