Finite Group Databasebeta

← Group #10690189

Character table — Group #10690189

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order1222222222223666666644444444666612121212121212122266668888888812121212242424242424242424242424242424244444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111-1-1-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ10111-1-1-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ11111-1-1-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ12111-1-1-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ13111-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ14111-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ15111-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ16111-1-1-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222200000000-2-2-2-200000000000000000000000000000000
χ19222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2111100000000-1-1-1-133−3−333−3−333−3−333−3−30000000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2111100000000-1-1-1-1−3−333−3−333−3−333−3−3330000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-1-1-1-100000000111133−3−333−3−3−3−333−3−3330000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-1-1-1-1000000001111−3−333−3−33333−3−333−3−30000000000000000
χ2722222222-2-2-2-22222222200002-22-2-2-2-2-222-2-222-2-200000000000000000000000000000000002-22-2000000000000
χ2822222222-2-2-2-22222222200002-22-2-2-2-2-222-2-222-2-20000000000000000000000000000000000-22-22000000000000
χ2922222222-2-2-2-2222222220000-22-22-2-2-2-2-2-222-2-222000000000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2222222220000-22-22-2-2-2-2-2-222-2-22200000000000000000000000000000000000000-22-2200000000
χ31222-2-2-2-222-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22222-22-2-2220000000022-2-200000000000000000000000000000000
χ32222-2-2-2-222-2-2222-2-2-2-222-2-222-2-22222-2-2-2-2-2-222222-222-2-200000000-2-22200000000000000000000000000000000
χ33222-2-2-2-222-2-22-1-11111-1-122-2-222-2-2-1-111-1-1-1-111112-2-1-1112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ34222-2-2-2-222-2-22-1-11111-1-122-2-222-2-2-1-111-1-1-1-111112-2-1-111−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ35222-2-2-2-222-2-22-1-11111-1-122-2-2-2-222-1-1111111-1-1-1-1-2211-1-100000000-1-111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ36222-2-2-2-222-2-22-1-11111-1-122-2-2-2-222-1-1111111-1-1-1-1-2211-1-100000000-1-111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ37222-2-2-2-222-2-22-1-11111-1-1-2-22222-2-2-1-111-1-1-1-11111-2211-1-12i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ38222-2-2-2-222-2-22-1-11111-1-1-2-22222-2-2-1-111-1-1-1-11111-2211-1-1−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ39222-2-2-2-222-2-22-1-11111-1-1-2-222-2-222-1-1111111-1-1-1-12-2-1-1110000000011-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ40222-2-2-2-222-2-22-1-11111-1-1-2-222-2-222-1-1111111-1-1-1-12-2-1-1110000000011-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ41222-2-2-2-22-222-222-2-2-2-22200002-2-22-2-22222-2-2-2-22200000000000000000000000000000000002i−2i−2i2i000000000000
χ42222-2-2-2-22-222-222-2-2-2-22200002-2-22-2-22222-2-2-2-2220000000000000000000000000000000000−2i2i2i−2i000000000000
χ43222-2-2-2-22-222-222-2-2-2-2220000-222-2-2-222-2-22222-2-2000000000000000000000000000000000000002i−2i−2i2i00000000
χ44222-2-2-2-22-222-222-2-2-2-2220000-222-2-2-222-2-22222-2-200000000000000000000000000000000000000−2i2i2i−2i00000000
χ4522-222-2-2-2-22-222222-2-2-2-22i−2i2i−2i00002-22-2000000000000002−22−2−i2i2−i2i22i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4622-222-2-2-2-22-222222-2-2-2-22i−2i2i−2i00002-22-200000000000000−22−22i2−i2i2−i22i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4722-222-2-2-2-22-222222-2-2-2-2−2i2i−2i2i00002-22-2000000000000002−22−2i2−i2i2−i2−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4822-222-2-2-2-22-222222-2-2-2-2−2i2i−2i2i00002-22-200000000000000−22−22−i2i2−i2i2−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ4922-222-2-2-2-22-22-1-1-1-111112i−2i2i−2i0000-11-113−33−33−33−300−i3i3−i3i32−22−2−i2i2−i2i2−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5022-222-2-2-2-22-22-1-1-1-111112i−2i2i−2i0000-11-113−33−33−33−300−i3i3−i3i3−22−22i2−i2i2−i2−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5122-222-2-2-2-22-22-1-1-1-111112i−2i2i−2i0000-11-11−33−33−33−3300i3−i3i3−i32−22−2−i2i2−i2i2−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5222-222-2-2-2-22-22-1-1-1-111112i−2i2i−2i0000-11-11−33−33−33−3300i3−i3i3−i3−22−22i2−i2i2−i2−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5322-222-2-2-2-22-22-1-1-1-11111−2i2i−2i2i0000-11-113−33−33−33−300i3−i3i3−i32−22−2i2−i2i2−i2i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5422-222-2-2-2-22-22-1-1-1-11111−2i2i−2i2i0000-11-113−33−33−33−300i3−i3i3−i3−22−22−i2i2−i2i2i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5522-222-2-2-2-22-22-1-1-1-11111−2i2i−2i2i0000-11-11−33−33−33−3300−i3i3−i3i32−22−2i2−i2i2−i2i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5622-222-2-2-2-22-22-1-1-1-11111−2i2i−2i2i0000-11-11−33−33−33−3300−i3i3−i3i3−22−22−i2i2−i2i2i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5722-2-2-222-2-2-22222-2-222-2-22i−2i−2i2i00002-2-2200000000000000−i2i2i2−i2−222−22i−2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ5822-2-2-222-2-2-22222-2-222-2-22i−2i−2i2i00002-2-2200000000000000i2−i2−i2i22−2−222i−2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ5922-2-2-222-2-2-22222-2-222-2-2−2i2i2i−2i00002-2-2200000000000000−i2i2i2−i22−2−22−2i2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ6022-2-2-222-2-2-22222-2-222-2-2−2i2i2i−2i00002-2-2200000000000000i2−i2−i2i2−222−2−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ6122-2-2-222-2-2-222-1-111-1-1112i−2i−2i2i0000-111-13−33−3−33−3300−i3i3i3−i3−i2i2i2−i2−222−2−iii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ6222-2-2-222-2-2-222-1-111-1-1112i−2i−2i2i0000-111-13−33−3−33−3300−i3i3i3−i3i2−i2−i2i22−2−22−iii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ6322-2-2-222-2-2-222-1-111-1-1112i−2i−2i2i0000-111-1−33−333−33−300i3−i3−i3i3−i2i2i2−i2−222−2−iii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ6422-2-2-222-2-2-222-1-111-1-1112i−2i−2i2i0000-111-1−33−333−33−300i3−i3−i3i3i2−i2−i2i22−2−22−iii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ6522-2-2-222-2-2-222-1-111-1-111−2i2i2i−2i0000-111-13−33−3−33−3300i3−i3−i3i3−i2i2i2−i22−2−22i−i−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ6622-2-2-222-2-2-222-1-111-1-111−2i2i2i−2i0000-111-13−33−3−33−3300i3−i3−i3i3i2−i2−i2i2−222−2i−i−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ6722-2-2-222-2-2-222-1-111-1-111−2i2i2i−2i0000-111-1−33−333−33−300−i3i3i3−i3−i2i2i2−i22−2−22i−i−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ6822-2-2-222-2-2-222-1-111-1-111−2i2i2i−2i0000-111-1−33−333−33−300−i3i3i3−i3i2−i2−i2i2−222−2i−i−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ6944444444-4-4-4-4-2-2-2-2-2-2-2-200004-44-42222-2-222-2-22200000000000000000000000000000000000000000000000000
χ7044444444-4-4-4-4-2-2-2-2-2-2-2-20000-44-44222222-2-222-2-200000000000000000000000000000000000000000000000000
χ71444-4-4-4-44-444-4-2-22222-2-200004-4-4422-2-2-2-22222-2-200000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-444-4-2-22222-2-20000-444-422-2-222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7344-444-4-4-44-44-44444-4-4-4-400000000-44-440000000000000000000000000000000000000000000000000000000000
χ7444-444-4-4-44-44-4-2-2-2-22222000000002-22-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ7544-444-4-4-44-44-4-2-2-2-22222000000002-22-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ7644-4-4-444-444-4-444-4-444-4-400000000-444-40000000000000000000000000000000000000000000000000000000000
χ7744-4-4-444-444-4-4-2-222-2-222000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ7844-4-4-444-444-4-4-2-222-2-222000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ794-444-44-4-400004-44-44-44-40000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ804-444-44-4-400004-44-44-44-4000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ814-44-44-44-400004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ824-44-44-44-400004-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
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χ854-4-4-444-4400004-4-444-4-44000000000000000000000000000000000000000000000000000000000000002-2-220000
χ864-4-4-444-4400004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000-222-20000
χ878-888-88-8-80000-44-44-44-440000000000000000000000000000000000000000000000000000000000000000000000
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χ908-8-8-888-880000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000

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