Finite Group Databasebeta

← Group #11774629

Character table — Group #11774629

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111111122222222222222222222444444444444444444448888888888888888888812121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636
order1222444433444466666612121212121212123444466612121212121212121212121212121212121212121212121212121212121212128888888824242424242424242424242424242424444488882424242424242424222444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1
χ611111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-111
χ711111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-111-111
χ811111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-1
χ91111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−iii−i−iii−i−i111-1-1-1
χ101111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111i−i−iiii−i−i−i−iii-1-1-1111
χ111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−iii−i−i−iiiii−i−i-1-1-1111
χ121111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii−i−iii−i−iii111-1-1-1
χ131111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−ii−i−iii−i−iii1-1-1-111
χ141111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111−iii−i−i−iiiii−i−i-1111-1-1
χ151111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111i−i−iiii−i−i−i−iii-1111-1-1
χ161111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−iii−i−iii−i−i1-1-1-111
χ172222222222-2-2-2-22222222222222220000222-2-2-2-22222-2-2-2-200000000-2-2-2-2000000000000000000000000000000002222000000000000-200-200
χ182222222222-2-2-2-22222222222222220000222-2-2-2-22222-2-2-2-200000000-2-2-2-200000000000000000000000000000000-2-2-2-2000000000000200200
χ19222222222-122222-122-1-122-1-122-1-1-12222-1-1-122-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000220000-1-1-1-1000000
χ20222222222-122222-122-1-122-1-122-1-1-12222-1-1-122-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000-2-200001111000000
χ21222222222-122222-122-1-122-1-122-1-1-1-2-2-2-2-1-1-122-1-1-1-1-1-122-1-1-2-211-2-211-1-1-1-1111111110000222200000000-1-1-1-1-1-1-1-1000000-2-200001111000000
χ22222222222-122222-122-1-122-1-122-1-1-1-2-2-2-2-1-1-122-1-1-1-1-1-122-1-1-2-211-2-211-1-1-1-1111111110000-2-2-2-20000000011111111000000220000-1-1-1-1000000
χ2322222222-122222-12-1-122-1-122-1-122-12222-1-1-1-1-122-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000002200-1-1-1-10000000000
χ2422222222-122222-12-1-122-1-122-1-122-12222-1-1-1-1-122-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000-2-20011110000000000
χ2522222222-122222-12-1-122-1-122-1-122-1-2-2-2-2-1-1-1-1-122-1-1-1-1-1-12211-2-211-2-2-1-1-1-11111111122220000-1-1-1-1-1-1-1-1000000000000-2-20011110000000000
χ2622222222-122222-12-1-122-1-122-1-122-1-2-2-2-2-1-1-1-1-122-1-1-1-1-1-12211-2-211-2-2-1-1-1-111111111-2-2-2-20000111111110000000000002200-1-1-1-10000000000
χ272222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-220000222-2-2-2-2-2-2-2-2222200000000-2-2220000000000000000000000000000000022-2-2000000000000-200200
χ282222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-220000222-2-2-2-2-2-2-2-2222200000000-2-22200000000000000000000000000000000-2-222000000000000200-200
χ292222-2-2-2-22-122-2-22-122-1-1-2-211-2-211-122-2-2-1-1-122-1-11111-2-21122-1-1-2-211-1-111-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii0000002i−2i0000−i−iii000000
χ302222-2-2-2-22-122-2-22-122-1-1-2-211-2-211-122-2-2-1-1-122-1-11111-2-21122-1-1-2-211-1-111-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i000000−2i2i0000ii−i−i000000
χ312222-2-2-2-22-122-2-22-122-1-1-2-211-2-211-1-2-222-1-1-122-1-11111-2-211-2-21122-1-1-1-1111111-1-1-1-100002i2i−2i−2i00000000−i−i−i−iiiii000000−2i2i0000ii−i−i000000
χ322222-2-2-2-22-122-2-22-122-1-1-2-211-2-211-1-2-222-1-1-122-1-11111-2-211-2-21122-1-1-1-1111111-1-1-1-10000−2i−2i2i2i00000000iiii−i−i−i−i0000002i−2i0000−i−iii000000
χ332222-2-2-2-2-1222-2-2-12-1-12211-2-211-2-2-122-2-2-1-1-1-1-122111111-2-2-1-12211-2-2-1-111-1-1-1-111112i2i−2i−2i0000−i−i−i−iiiii0000000000002i−2i00−i−iii0000000000
χ342222-2-2-2-2-1222-2-2-12-1-12211-2-211-2-2-122-2-2-1-1-1-1-122111111-2-2-1-12211-2-2-1-111-1-1-1-11111−2i−2i2i2i0000iiii−i−i−i−i000000000000−2i2i00ii−i−i0000000000
χ352222-2-2-2-2-1222-2-2-12-1-12211-2-211-2-2-1-2-222-1-1-1-1-122111111-2-211-2-2-1-122-1-1111111-1-1-1-12i2i−2i−2i0000−i−i−i−iiiii000000000000−2i2i00ii−i−i0000000000
χ362222-2-2-2-2-1222-2-2-12-1-12211-2-211-2-2-1-2-222-1-1-1-1-122111111-2-211-2-2-1-122-1-1111111-1-1-1-1−2i−2i2i2i0000iiii−i−i−i−i0000000000002i−2i00−i−iii0000000000
χ3722-2-22i2i−2i−2i222-22i−2i-2-22-22-22i−2i2i−2i2i−2i2i−2i20000-22-22-22-22i2i−2i−2i2i−2i2i−2i000000002-22i−2i00000000000000000000000000000000000000000000000002-202i−2i
χ3822-2-22i2i−2i−2i222-22i−2i-2-22-22-22i−2i2i−2i2i−2i2i−2i20000-22-22-22-22i2i−2i−2i2i−2i2i−2i000000002-22i−2i0000000000000000000000000000000000000000000000000-220−2i2i
χ3922-2-22i2i−2i−2i22-22−2i2i-2-22-22-22i−2i2i−2i2i−2i2i−2i22-22i−2i-22-2-22-222i2i−2i−2i−2i2i−2i2i2-22-22i−2i2i−2i-22−2i2i22-2-22i2i−2i−2i0000000000000000000000000000000000000000000000
χ4022-2-22i2i−2i−2i22-22−2i2i-2-22-22-22i−2i2i−2i2i−2i2i−2i2-22−2i2i-22-2-22-222i2i−2i−2i−2i2i−2i2i-22-22−2i2i−2i2i-22−2i2i-2-222−2i−2i2i2i0000000000000000000000000000000000000000000000
χ4122-2-22i2i−2i−2i2-1-22−2i2i-212-2-112i−2i−ii2i−2i−ii-12-22i−2i1-11-221-1−i−iii−2i2ii−i2-2-112i−2i−ii1-1i−i-1-111−i−iii0000000000000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ4222-2-22i2i−2i−2i2-1-22−2i2i-212-2-112i−2i−ii2i−2i−ii-12-22i−2i1-11-221-1−i−iii−2i2ii−i2-2-112i−2i−ii1-1i−i-1-111−i−iii0000000000000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ4322-2-22i2i−2i−2i2-1-22−2i2i-212-2-112i−2i−ii2i−2i−ii-1-22−2i2i1-11-221-1−i−iii−2i2ii−i-221-1−2i2ii−i1-1i−i11-1-1ii−i−i0000000000000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ4422-2-22i2i−2i−2i2-1-22−2i2i-212-2-112i−2i−ii2i−2i−ii-1-22−2i2i1-11-221-1−i−iii−2i2ii−i-221-1−2i2ii−i1-1i−i11-1-1ii−i−i0000000000000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ4522-2-22i2i−2i−2i-12-22−2i2i1-2-112-2−ii2i−2i−ii2i−2i-12-22i−2i1-111-1-22−i−iiii−i−2i2i-112-2−ii2i−2i1-1i−i-1-111−i−iii00000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ230000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4622-2-22i2i−2i−2i-12-22−2i2i1-2-112-2−ii2i−2i−ii2i−2i-12-22i−2i1-111-1-22−i−iiii−i−2i2i-112-2−ii2i−2i1-1i−i-1-111−i−iii00000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ230000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4722-2-22i2i−2i−2i-12-22−2i2i1-2-112-2−ii2i−2i−ii2i−2i-1-22−2i2i1-111-1-22−i−iiii−i−2i2i1-1-22i−i−2i2i1-1i−i11-1-1ii−i−i00000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ230000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4822-2-22i2i−2i−2i-12-22−2i2i1-2-112-2−ii2i−2i−ii2i−2i-1-22−2i2i1-111-1-22−i−iiii−i−2i2i1-1-22i−i−2i2i1-1i−i11-1-1ii−i−i00000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ230000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4922-2-2−2i−2i2i2i222-2−2i2i-2-22-22-2−2i2i−2i2i−2i2i−2i2i20000-22-22-22-2−2i−2i2i2i−2i2i−2i2i000000002-2−2i2i00000000000000000000000000000000000000000000000002-20−2i2i
χ5022-2-2−2i−2i2i2i222-2−2i2i-2-22-22-2−2i2i−2i2i−2i2i−2i2i20000-22-22-22-2−2i−2i2i2i−2i2i−2i2i000000002-2−2i2i0000000000000000000000000000000000000000000000000-2202i−2i
χ5122-2-2−2i−2i2i2i22-222i−2i-2-22-22-2−2i2i−2i2i−2i2i−2i2i22-2−2i2i-22-2-22-22−2i−2i2i2i2i−2i2i−2i2-22-2−2i2i−2i2i-222i−2i22-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000
χ5222-2-2−2i−2i2i2i22-222i−2i-2-22-22-2−2i2i−2i2i−2i2i−2i2i2-222i−2i-22-2-22-22−2i−2i2i2i2i−2i2i−2i-22-222i−2i2i−2i-222i−2i-2-2222i2i−2i−2i0000000000000000000000000000000000000000000000
χ5322-2-2−2i−2i2i2i2-1-222i−2i-212-2-11−2i2ii−i−2i2ii−i-12-2−2i2i1-11-221-1ii−i−i2i−2i−ii2-2-11−2i2ii−i1-1−ii-1-111ii−i−i0000000000000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ5422-2-2−2i−2i2i2i2-1-222i−2i-212-2-11−2i2ii−i−2i2ii−i-12-2−2i2i1-11-221-1ii−i−i2i−2i−ii2-2-11−2i2ii−i1-1−ii-1-111ii−i−i0000000000000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ5522-2-2−2i−2i2i2i2-1-222i−2i-212-2-11−2i2ii−i−2i2ii−i-1-222i−2i1-11-221-1ii−i−i2i−2i−ii-221-12i−2i−ii1-1−ii11-1-1−i−iii0000000000000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ5622-2-2−2i−2i2i2i2-1-222i−2i-212-2-11−2i2ii−i−2i2ii−i-1-222i−2i1-11-221-1ii−i−i2i−2i−ii-221-12i−2i−ii1-1−ii11-1-1−i−iii0000000000000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ5722-2-2−2i−2i2i2i-12-222i−2i1-2-112-2i−i−2i2ii−i−2i2i-12-2−2i2i1-111-1-22ii−i−i−ii2i−2i-112-2i−i−2i2i1-1−ii-1-111ii−i−i00000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ130000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ5822-2-2−2i−2i2i2i-12-222i−2i1-2-112-2i−i−2i2ii−i−2i2i-12-2−2i2i1-111-1-22ii−i−i−ii2i−2i-112-2i−i−2i2i1-1−ii-1-111ii−i−i00000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ130000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ5922-2-2−2i−2i2i2i-12-222i−2i1-2-112-2i−i−2i2ii−i−2i2i-1-222i−2i1-111-1-22ii−i−i−ii2i−2i1-1-22−ii2i−2i1-1−ii11-1-1−i−iii00000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ130000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ6022-2-2−2i−2i2i2i-12-222i−2i1-2-112-2i−i−2i2ii−i−2i2i-1-222i−2i1-111-1-22ii−i−i−ii2i−2i1-1-22−ii2i−2i1-1−ii11-1-1−i−iii00000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ130000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ612-2-222-22-222000022-2-2-2-222-2-2-2-222200002-2-200002-22-20000000000000000000000002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i22i−2i2i−2i000000000000000000
χ622-2-222-22-222000022-2-2-2-222-2-2-2-222200002-2-200002-22-20000000000000000000000002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.