Finite Group Databasebeta

← Group #10896496

Character table — Group #10896496

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222223444444444444666666612121212121212124444444412121212121212121212121212121212121212121212121288888888242424242424242424242424242424244444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ6111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ1011111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1211111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1
χ1311111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1411111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1
χ1611111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ17222222222-2-222222222-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-222222222-2-2-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−30000000000000000
χ3022222222-1-2-222222222-2-2-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−3330000000000000000
χ3122222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ3222222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ37222-2-2-22-222222-2-20000-2-2222-2-2-2-22222-2-2-2-200002-20022-2-222-2-200000000000000000000000000000000000000000000002-22-2000000
χ38222-2-2-22-222222-2-20000-2-2222-2-2-2-22222-2-2-2-200002-20022-2-222-2-20000000000000000000000000000000000000000000000-22-22000000
χ39222-2-2-22-2222-2-2220000-2-2222-2-2-2-22222-2-2-2-20000-2200-2-222-2-22200000000000000000000000000000000000000000000002-2-22000000
χ40222-2-2-22-2222-2-2220000-2-2222-2-2-2-22222-2-2-2-20000-2200-2-222-2-2220000000000000000000000000000000000000000000000-222-2000000
χ41222-2-2-22-22-2-222-2-2000022222-2-2-2-2-2-2-2-222220000-220022-2-2-2-22200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ42222-2-2-22-22-2-222-2-2000022222-2-2-2-2-2-2-2-222220000-220022-2-2-2-2220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ43222-2-2-22-22-2-2-2-222000022222-2-2-2-2-2-2-2-2222200002-200-2-22222-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ44222-2-2-22-22-2-2-2-222000022222-2-2-2-2-2-2-2-2222200002-200-2-22222-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ4522-22-2-2-222002-22-22i2i−2i−2i002-2-222-2-200000000002i−2i00002-22-200002i2i−2i−2i00002i2i−2i−2i00002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4622-22-2-2-222002-22-22i2i−2i−2i002-2-222-2-200000000002i−2i00002-22-200002i2i−2i−2i00002i2i−2i−2i0000−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4722-22-2-2-222002-22-2−2i−2i2i2i002-2-222-2-20000000000−2i2i00002-22-20000−2i−2i2i2i0000−2i−2i2i2i00002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4822-22-2-2-222002-22-2−2i−2i2i2i002-2-222-2-20000000000−2i2i00002-22-20000−2i−2i2i2i0000−2i−2i2i2i0000−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ4922-22-2-2-22200-22-222i2i−2i−2i002-2-222-2-20000000000−2i2i0000-22-2200002i2i−2i−2i0000−2i−2i2i2i00002−2−22−i2i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ5022-22-2-2-22200-22-222i2i−2i−2i002-2-222-2-20000000000−2i2i0000-22-2200002i2i−2i−2i0000−2i−2i2i2i0000−222−2i2−i2−i2i2−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5122-22-2-2-22200-22-22−2i−2i2i2i002-2-222-2-200000000002i−2i0000-22-220000−2i−2i2i2i00002i2i−2i−2i00002−2−22i2−i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ5222-22-2-2-22200-22-22−2i−2i2i2i002-2-222-2-200000000002i−2i0000-22-220000−2i−2i2i2i00002i2i−2i−2i0000−222−2−i2i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ5322-22-2-2-22-1002-22-22i2i−2i−2i00-111-1-11133−3−333−3−3002i−2i0000-11-113−33−3−i−iii−i3−i3i3i3−i−iii−i3−i3i3i32−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5422-22-2-2-22-1002-22-22i2i−2i−2i00-111-1-11133−3−333−3−3002i−2i0000-11-113−33−3−i−iii−i3−i3i3i3−i−iii−i3−i3i3i3−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5522-22-2-2-22-1002-22-22i2i−2i−2i00-111-1-111−3−333−3−333002i−2i0000-11-11−33−33−i−iiii3i3−i3−i3−i−iiii3i3−i3−i32−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5622-22-2-2-22-1002-22-22i2i−2i−2i00-111-1-111−3−333−3−333002i−2i0000-11-11−33−33−i−iiii3i3−i3−i3−i−iiii3i3−i3−i3−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5722-22-2-2-22-1002-22-2−2i−2i2i2i00-111-1-11133−3−333−3−300−2i2i0000-11-113−33−3ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i32−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5822-22-2-2-22-1002-22-2−2i−2i2i2i00-111-1-11133−3−333−3−300−2i2i0000-11-113−33−3ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i3−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5922-22-2-2-22-1002-22-2−2i−2i2i2i00-111-1-111−3−333−3−33300−2i2i0000-11-11−33−33ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i32−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6022-22-2-2-22-1002-22-2−2i−2i2i2i00-111-1-111−3−333−3−33300−2i2i0000-11-11−33−33ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i3−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ6122-22-2-2-22-100-22-222i2i−2i−2i00-111-1-11133−3−333−3−300−2i2i00001-11-1−33−33−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i32−2−22−i2i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ6222-22-2-2-22-100-22-222i2i−2i−2i00-111-1-11133−3−333−3−300−2i2i00001-11-1−33−33−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i3−222−2i2−i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ6322-22-2-2-22-100-22-222i2i−2i−2i00-111-1-111−3−333−3−33300−2i2i00001-11-13−33−3−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i32−2−22−i2i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6422-22-2-2-22-100-22-222i2i−2i−2i00-111-1-111−3−333−3−33300−2i2i00001-11-13−33−3−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i3−222−2i2−i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ6522-22-2-2-22-100-22-22−2i−2i2i2i00-111-1-11133−3−333−3−3002i−2i00001-11-1−33−33ii−i−ii3i3−i3−i3−i−iii−i3−i3i3i32−2−22i2−i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
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χ1084-4-4-4-4444-2000000-444-40022-2-222-2−232323−23−232323−2300000000000000002-2-22−232323−23000000000000000000000000000000000000000000000000

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