Finite Group Databasebeta

← Group #11796956

Character table — Group #11796956

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222222222222334444444444444444444444444444446666666666666888888888888888881212121212121212121212121212121212242424244848484872727272
order1223344668812122424242444366681212121212161616162424242424242424484848484848484822466881212242424246122424244848484848484848484848486812161616162424484848484848484822886624244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ411111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ511111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-111
χ811111111111111111-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-11111-1-1
χ911-1111-111-1-111-1-1-1-1111-1-111-1111-1ii−i−i11-1-1-1-1-1-1iiii−i−i−i−i1-1-111-1-111-1-1-1-1-1-1111iiiiii−i−i−i−i−i−i-11-1ii−i−i11iiii−i−i−i−i1-1i−i1-1i−i1-1i−i
χ1011-1111-111-1-111-1-1-1-1111-1-111-1111-1ii−i−i11-1-1-1-1-1-1iiii−i−i−i−i1-1-111-1-111-1-1-1-1-1-1111iiiiii−i−i−i−i−i−i-11-1ii−i−i11iiii−i−i−i−i-11−ii-11−ii-11−ii
χ1111-1111-111-1-111-1-1-1-1111-1-111-1111-1−i−iii11-1-1-1-1-1-1−i−i−i−iiiii1-1-111-1-111-1-1-1-1-1-1111−i−i−i−i−i−iiiiiii-11-1−i−iii11−i−i−i−iiiii1-1−ii1-1−ii1-1−ii
χ1211-1111-111-1-111-1-1-1-1111-1-111-1111-1−i−iii11-1-1-1-1-1-1−i−i−i−iiiii1-1-111-1-111-1-1-1-1-1-1111−i−i−i−i−i−iiiiiii-11-1−i−iii11−i−i−i−iiiii-11i−i-11i−i-11i−i
χ1311-1111-111-1-111-1-1-1-1-1-11-1-111-1111-1ii−i−i11-1-1-1-1-1-1iiii−i−i−i−i-111-1-111-1-11111-1-1111iiiiii−i−i−i−i−i−i1-11−i−iii-1-1−i−i−i−iiiii1-1i−i1-1i−i-11−ii
χ1411-1111-111-1-111-1-1-1-1-1-11-1-111-1111-1ii−i−i11-1-1-1-1-1-1iiii−i−i−i−i-111-1-111-1-11111-1-1111iiiiii−i−i−i−i−i−i1-11−i−iii-1-1−i−i−i−iiiii-11−ii-11−ii1-1i−i
χ1511-1111-111-1-111-1-1-1-1-1-11-1-111-1111-1−i−iii11-1-1-1-1-1-1−i−i−i−iiiii-111-1-111-1-11111-1-1111−i−i−i−i−i−iiiiiii1-11ii−i−i-1-1iiii−i−i−i−i1-1−ii1-1−ii-11i−i
χ1611-1111-111-1-111-1-1-1-1-1-11-1-111-1111-1−i−iii11-1-1-1-1-1-1−i−i−i−iiiii-111-1-111-1-11111-1-1111−i−i−i−i−i−iiiiiii1-11ii−i−i-1-1iiii−i−i−i−i-11i−i-11i−i1-1−ii
χ17222222222-2-222-2-2-2-2222222-2222220000-2-2-2-2-2-2-2-20000000022222-2-222-2-2-2-222-2-2-20000000000002-220000-2-200000000000000000000
χ18222222222-2-222-2-2-2-2-2-22222-2222220000-2-2-2-2-2-2-2-200000000-2-2-2-2-222-2-2222222-2-2-2000000000000-22-200002200000000000000000000
χ1922222-2-22200-2-200002222220-2-2-2-2-2−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i2-2-22-2-2002200002-2000−i2−i2−i2i2i2i2−i2−i2−i2i2i2i2-202−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2000000000000
χ2022222-2-22200-2-200002222220-2-2-2-2-2i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i2-2-22-2-2002200002-2000i2i2i2−i2−i2−i2i2i2i2−i2−i2−i2-202i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2000000000000
χ2122222-2-22200-2-20000-2-222220-2-2-2-2-2−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i222-22200-2-200002-2000−i2−i2−i2i2i2i2−i2−i2−i2i2i2i220-2i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2000000000000
χ2222222-2-22200-2-20000-2-222220-2-2-2-2-2i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i222-22200-2-200002-2000i2i2i2−i2−i2−i2i2i2i2−i2−i2−i220-2−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2000000000000
χ232222-122-122222222200-12-1-122-1-1-1-1222222-1-1-1-1-1-1222222220000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000002222-1-1-1-10000
χ242222-122-122222222200-12-1-122-1-1-1-1222222-1-1-1-1-1-1222222220000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000-2-2-2-211110000
χ252222-122-122222222200-12-1-122-1-1-1-1-2-2-2-222-1-1-1-1-1-1-2-2-2-2-2-2-2-20000000000000-1-1-1-1-11111111111110000000000000000022-2-2-1-1110000
χ262222-122-122222222200-12-1-122-1-1-1-1-2-2-2-222-1-1-1-1-1-1-2-2-2-2-2-2-2-20000000000000-1-1-1-1-111111111111100000000000000000-2-22211-1-10000
χ27222-12222-122-1-1-1-1-1-122-1-12-12-12-1-122222-1-122-1-1-1-1-1-1-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-12-1-12-1-12-1-12-1-12-1-1-12-12222-1-1-1-1-1-1-1-1-1-1000000000000
χ28222-12222-122-1-1-1-1-1-122-1-12-12-12-1-12-2-2-2-2-1-122-1-1-1-111111111222-1-122-1-1-1-1-1-1-1-12-1-1-211-211-211-211-12-1-2-2-2-2-1-111111111000000000000
χ29222-12222-122-1-1-1-1-1-1-2-2-1-12-12-12-1-122222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211-2-2111111-1-12-1-12-1-12-1-12-1-12-1-11-21-2-2-2-21111111111000000000000
χ30222-12222-122-1-1-1-1-1-1-2-2-1-12-12-12-1-12-2-2-2-2-1-122-1-1-1-111111111-2-2-211-2-2111111-1-12-1-1-211-211-211-2111-21222211-1-1-1-1-1-1-1-1000000000000
χ31222-12222-1-2-2-1-1111122-1-12-1-2-12-1-12000011-2-211113−33−33−33−3222-1-1-2-2-1-11111-1-1-21103−303−303−303−3-1-2-10000113−33−33−33−3000000000000
χ32222-12222-1-2-2-1-1111122-1-12-1-2-12-1-12000011-2-21111−33−33−33−33222-1-1-2-2-1-11111-1-1-2110−330−330−330−33-1-2-1000011−33−33−33−33000000000000
χ33222-12222-1-2-2-1-11111-2-2-1-12-1-2-12-1-12000011-2-211113−33−33−33−3-2-2-2112211-1-1-1-1-1-1-21103−303−303−303−31210000-1-1−33−33−33−33000000000000
χ34222-12222-1-2-2-1-11111-2-2-1-12-1-2-12-1-12000011-2-21111−33−33−33−33-2-2-2112211-1-1-1-1-1-1-2110−330−330−330−331210000-1-13−33−33−33−3000000000000
χ35222-12-2-22-1001133−3−322-1-12-101-211-2−i2i2−i2i23−30033−3−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23-2-221100-1-133−3−3-1103−3−i2ζ5+ζ7ζ13+ζ23i2−ζ5−ζ7−ζ13−ζ23−i2ζ5+ζ7ζ13+ζ23i2−ζ5−ζ7−ζ13−ζ2310-1−i2i2−i2i23−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ36222-12-2-22-1001133−3−322-1-12-101-211-2i2−i2i2−i23−30033−3−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23-2-221100-1-133−3−3-1103−3i2−ζ5−ζ7−ζ13−ζ23−i2ζ5+ζ7ζ13+ζ23i2−ζ5−ζ7−ζ13−ζ23−i2ζ5+ζ7ζ13+ζ2310-1i2−i2i2−i23−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ37222-12-2-22-1001133−3−3-2-2-1-12-101-211-2−i2i2−i2i23−30033−3−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2322-2-1-10011−3−333-1103−3−i2ζ5+ζ7ζ13+ζ23i2−ζ5−ζ7−ζ13−ζ23−i2ζ5+ζ7ζ13+ζ23i2−ζ5−ζ7−ζ13−ζ23-101i2−i2i2−i2−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000
χ38222-12-2-22-1001133−3−3-2-2-1-12-101-211-2i2−i2i2−i23−30033−3−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2322-2-1-10011−3−333-1103−3i2−ζ5−ζ7−ζ13−ζ23−i2ζ5+ζ7ζ13+ζ23i2−ζ5−ζ7−ζ13−ζ23−i2ζ5+ζ7ζ13+ζ23-101−i2i2−i2i2−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ39222-12-2-22-10011−3−33322-1-12-101-211-2−i2i2−i2i2−3300−3−333ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7-2-221100-1-1−3−333-110−33−i2ζ13+ζ23ζ5+ζ7i2−ζ13−ζ23−ζ5−ζ7−i2ζ13+ζ23ζ5+ζ7i2−ζ13−ζ23−ζ5−ζ710-1−i2i2−i2i2−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ40222-12-2-22-10011−3−33322-1-12-101-211-2i2−i2i2−i2−3300−3−333−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7-2-221100-1-1−3−333-110−33i2−ζ13−ζ23−ζ5−ζ7−i2ζ13+ζ23ζ5+ζ7i2−ζ13−ζ23−ζ5−ζ7−i2ζ13+ζ23ζ5+ζ710-1i2−i2i2−i2−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ41222-12-2-22-10011−3−333-2-2-1-12-101-211-2−i2i2−i2i2−3300−3−333ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ722-2-1-1001133−3−3-110−33−i2ζ13+ζ23ζ5+ζ7i2−ζ13−ζ23−ζ5−ζ7−i2ζ13+ζ23ζ5+ζ7i2−ζ13−ζ23−ζ5−ζ7-101i2−i2i2−i23−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
χ42222-12-2-22-10011−3−333-2-2-1-12-101-211-2i2−i2i2−i2−3300−3−333−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ722-2-1-1001133−3−3-110−33i2−ζ13−ζ23−ζ5−ζ7−i2ζ13+ζ23ζ5+ζ7i2−ζ13−ζ23−ζ5−ζ7−i2ζ13+ζ23ζ5+ζ7-101−i2i2−i2i23−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ4322-2222-22222222222222-2-22-2-2222-20000-2-2222222000000002-2-22222222222-2-2-2-2-2000000000000-2-2-20000-2-200000000000000000000
χ4422-2222-22222222222-2-22-2-22-2-2222-20000-2-222222200000000-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000022200002200000000000000000000
χ4522-222-222200-2-20000222-2-2202-2-2-222−2−220000000022−2−2−2−222-22-2-2-200220000-22000222−2−2−2−2−2−222220-22−2−220022−2−2−2−222000000000000
χ4622-222-222200-2-20000222-2-2202-2-2-22−222−200000000−2−22222−2−2-22-2-2-200220000-22000−2−2−2222222−2−2−220-2−222−200−2−22222−2−2000000000000
χ4722-222-222200-2-20000-2-22-2-2202-2-2-222−2−220000000022−2−2−2−2222-222200-2-20000-22000222−2−2−2−2−2−2222-202−222−200−2−22222−2−2000000000000
χ4822-222-222200-2-20000-2-22-2-2202-2-2-22−222−200000000−2−22222−2−22-222200-2-20000-22000−2−2−2222222−2−2−2-2022−2−220022−2−2−2−222000000000000
χ4922-22-12-2-12-2-222-2-2-2-200-1-21-12-2-1-1-112i2i−2i−2i221111112i2i2i2i−2i−2i−2i−2i000000000000011-1-1-1−i−i−i−i−i−iiiiiii000000000000000002-22i−2i-11−ii0000
χ5022-22-12-2-12-2-222-2-2-2-200-1-21-12-2-1-1-112i2i−2i−2i221111112i2i2i2i−2i−2i−2i−2i000000000000011-1-1-1−i−i−i−i−i−iiiiiii00000000000000000-22−2i2i1-1i−i0000
χ5122-22-12-2-12-2-222-2-2-2-200-1-21-12-2-1-1-11−2i−2i2i2i22111111−2i−2i−2i−2i2i2i2i2i000000000000011-1-1-1iiiiii−i−i−i−i−i−i000000000000000002-2−2i2i-11i−i0000
χ5222-22-12-2-12-2-222-2-2-2-200-1-21-12-2-1-1-11−2i−2i2i2i22111111−2i−2i−2i−2i2i2i2i2i000000000000011-1-1-1iiiiii−i−i−i−i−i−i00000000000000000-222i−2i1-1−ii0000
χ5322-2-122-22-122-1-1-1-1-1-122-11-2-1-212-1-1-200001122-1-1-1-1−i3i3−i3i3i3−i3i3−i32-2-2-1-122-1-1-1-1-1-111-2110−i3i30−i3i30i3−i30i3−i31-21000011−i3i3−i3i3i3−i3i3−i3000000000000
χ5422-2-122-22-122-1-1-1-1-1-122-11-2-1-212-1-1-200001122-1-1-1-1i3−i3i3−i3−i3i3−i3i32-2-2-1-122-1-1-1-1-1-111-2110i3−i30i3−i30−i3i30−i3i31-21000011i3−i3i3−i3−i3i3−i3i3000000000000
χ5522-2-122-22-122-1-1-1-1-1-1-2-2-11-2-1-212-1-1-200001122-1-1-1-1−i3i3−i3i3i3−i3i3−i3-22211-2-211111111-2110−i3i30−i3i30i3−i30i3−i3-12-10000-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ5622-2-122-22-122-1-1-1-1-1-1-2-2-11-2-1-212-1-1-200001122-1-1-1-1i3−i3i3−i3−i3i3−i3i3-22211-2-211111111-2110i3−i30i3−i30−i3i30−i3i3-12-10000-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ5722-2-122-22-1-2-2-1-1111122-11-2-1212-1-1-22i2i−2i−2i-1-1-2-21111−i−i−i−iiiii2-2-2-1-1-2-2-1-11111112-1-12i−i−i2i−i−i−2iii−2iii1212i2i−2i−2i-1-1−i−i−i−iiiii000000000000
χ5822-2-122-22-1-2-2-1-1111122-11-2-1212-1-1-2−2i−2i2i2i-1-1-2-21111iiii−i−i−i−i2-2-2-1-1-2-2-1-11111112-1-1−2iii−2iii2i−i−i2i−i−i121−2i−2i2i2i-1-1iiii−i−i−i−i000000000000
χ5922-2-122-22-1-2-2-1-11111-2-2-11-2-1212-1-1-22i2i−2i−2i-1-1-2-21111−i−i−i−iiiii-222112211-1-1-1-1112-1-12i−i−i2i−i−i−2iii−2iii-1-2-1−2i−2i2i2i11iiii−i−i−i−i000000000000
χ6022-2-122-22-1-2-2-1-11111-2-2-11-2-1212-1-1-2−2i−2i2i2i-1-1-2-21111iiii−i−i−i−i-222112211-1-1-1-1112-1-1−2iii−2iii2i−i−i2i−i−i-1-2-12i2i−2i−2i11−i−i−i−iiiii000000000000
χ6122-2-12-222-1001133−3−322-11-2-10-1-21122−2−22−330033−3−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23-22-21100-1-133−3−31-10−332ζ5−ζ7ζ13−ζ23−2−ζ5+ζ7−ζ13+ζ23−2−ζ5+ζ7−ζ13+ζ232ζ5−ζ7ζ13−ζ23-1012−2−22−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ6222-2-12-222-1001133−3−322-11-2-10-1-2112−222−2−330033−3−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23-22-21100-1-133−3−31-10−33−2−ζ5+ζ7−ζ13+ζ232ζ5−ζ7ζ13−ζ232ζ5−ζ7ζ13−ζ23−2−ζ5+ζ7−ζ13+ζ23-101−222−2−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
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χ1088-80-4-40044−4242−4343−4ζ13+4ζ234ζ13−4ζ23−4ζ5+4ζ74ζ5−4ζ700200-200023−23000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.