Finite Group Databasebeta

← Group #10830652

Character table — Group #10830652

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222344444444666666612121212121212122244448888888812121212121212122424242424242424242424242424242424666688881212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111111111111111-1-111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ611111111111111111111111111111111-1-111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ711111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ9111111111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11-1
χ10111111111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-11
χ11111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-11
χ12111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ13111111111-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-1-11
χ14111111111-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111-1
χ15111111111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1111-1
χ16111111111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ172222222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222000000002222-2-2-2-20000000000000000-2-222-2-20000-2-222000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-222000022-2-2000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-200000000-2-2-2-2222200000000000000002-222220000-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-222220000000000000000-22-2-2-2-200002222000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-21111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-22200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2-2-1-111000011-1-133−3−333−3−30000000000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-22200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2-2-1-111000011-1-1−3−333−3−3330000000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−32211-1-10000-1-111−3−333−3−3330000000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−333332211-1-10000-1-11133−3−333−3−30000000000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-22-1-11122-2-2-1-111-1-1-1-111110000000000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-22-1-111-2-222-1-1111111-1-1-1-10000000000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-211-1-1-2-22211-1-11111-1-1-1-10000000000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-211-1-122-2-211-1-1-1-1-1-111110000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-2-1-1-1-10000111133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-2-1-1-1-100001111−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-2211110000-1-1-1-1−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-2211110000-1-1-1-133−3−3−3−3330000000000000000
χ37222-2-2-2-222000022-2-222-2-2-2-222222-2-2-2-20000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000022-2-200002i−2i000000
χ38222-2-2-2-222000022-2-222-2-2-2-222222-2-2-2-20000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-2-2220000−2i2i000000
χ39222-2-2-2-222000022-2-222-2-2-2-222222-2-2-2-2000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000022-2-20000−2i2i000000
χ40222-2-2-2-222000022-2-222-2-2-2-222222-2-2-2-2000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-2-22200002i−2i000000
χ4122-2-22-22-222i2i−2i−2i00002-22-22-2-2000000002-2002i−2i−i2i2−i2i222−2−22i2i−2i−2i0000−i2i2−i2i2−i2i2−i2i222−2−222−2−2002-200−i2i22−2002i−2i−i2i2−i2i22−22−20000000000000000
χ4222-2-22-22-222i2i−2i−2i00002-22-22-2-2000000002-2002i−2ii2−i2i2−i2−2−2222i2i−2i−2i0000i2−i2i2−i2i2−i2i2−i2−2−222−2−222002-200i2−i2−22002i−2ii2−i2i2−i2−22−220000000000000000
χ4322-2-22-22-222i2i−2i−2i00002-22-22-2-200000000-2200−2i2i−i2i2−i2i222−2−22i2i−2i−2i0000−i2i2−i2i2−i2i2−i2i222−2−222−2−200-2200i2−i2−2200−2i2ii2−i2i2−i2−22−220000000000000000
χ4422-2-22-22-222i2i−2i−2i00002-22-22-2-200000000-2200−2i2ii2−i2i2−i2−2−2222i2i−2i−2i0000i2−i2i2−i2i2−i2i2−i2−2−222−2−22200-2200−i2i22−200−2i2i−i2i2−i2i22−22−20000000000000000
χ4522-2-22-22-22−2i−2i2i2i00002-22-22-2-2000000002-200−2i2i−i2i2−i2i2−2−222−2i−2i2i2i0000−i2i2−i2i2−i2i2−i2i2−2−222−2−222002-200−i2i2−2200−2i2i−i2i2−i2i2−22−220000000000000000
χ4622-2-22-22-22−2i−2i2i2i00002-22-22-2-2000000002-200−2i2ii2−i2i2−i222−2−2−2i−2i2i2i0000i2−i2i2−i2i2−i2i2−i222−2−222−2−2002-200i2−i22−200−2i2ii2−i2i2−i22−22−20000000000000000
χ4722-2-22-22-22−2i−2i2i2i00002-22-22-2-200000000-22002i−2i−i2i2−i2i2−2−222−2i−2i2i2i0000−i2i2−i2i2−i2i2−i2i2−2−222−2−22200-2200i2−i22−2002i−2ii2−i2i2−i22−22−20000000000000000
χ4822-2-22-22-22−2i−2i2i2i00002-22-22-2-200000000-22002i−2ii2−i2i2−i222−2−2−2i−2i2i2i0000i2−i2i2−i2i2−i2i2−i222−2−222−2−200-2200−i2i2−22002i−2i−i2i2−i2i2−22−220000000000000000
χ4922-2-22-22-2-12i2i−2i−2i0000-11-11-1113−33−33−33−32-2002i−2i−i2i2−i2i222−2−2−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700-11−i3i3−i2i22−23−3−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ5022-2-22-22-2-12i2i−2i−2i0000-11-11-1113−33−33−33−32-2002i−2ii2−i2i2−i2−2−222−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700-11−i3i3i2−i2−223−3−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5122-2-22-22-2-12i2i−2i−2i0000-11-11-1113−33−33−33−3-2200−2i2i−i2i2−i2i222−2−2−i−iii−i3−i3i3i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7001-1i3−i3i2−i2−22−33i−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5222-2-22-22-2-12i2i−2i−2i0000-11-11-1113−33−33−33−3-2200−2i2ii2−i2i2−i2−2−222−i−iii−i3−i3i3i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7001-1i3−i3−i2i22−2−33i−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ5322-2-22-22-2-12i2i−2i−2i0000-11-11-111−33−33−33−332-2002i−2i−i2i2−i2i222−2−2−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300-11i3−i3−i2i22−2−33−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ5422-2-22-22-2-12i2i−2i−2i0000-11-11-111−33−33−33−332-2002i−2ii2−i2i2−i2−2−222−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300-11i3−i3i2−i2−22−33−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5522-2-22-22-2-12i2i−2i−2i0000-11-11-111−33−33−33−33-2200−2i2i−i2i2−i2i222−2−2−i−iiii3i3−i3−i3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23001-1−i3i3i2−i2−223−3i−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5622-2-22-22-2-12i2i−2i−2i0000-11-11-111−33−33−33−33-2200−2i2ii2−i2i2−i2−2−222−i−iiii3i3−i3−i3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23001-1−i3i3−i2i22−23−3i−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ5722-2-22-22-2-1−2i−2i2i2i0000-11-11-1113−33−33−33−32-200−2i2i−i2i2−i2i2−2−222ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700-11i3−i3−i2i2−223−3i−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5822-2-22-22-2-1−2i−2i2i2i0000-11-11-1113−33−33−33−32-200−2i2ii2−i2i2−i222−2−2ii−i−ii3i3−i3−i3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700-11i3−i3i2−i22−23−3i−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ5922-2-22-22-2-1−2i−2i2i2i0000-11-11-1113−33−33−33−3-22002i−2i−i2i2−i2i2−2−222ii−i−ii3i3−i3−i3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7001-1−i3i3i2−i22−2−33−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.