Finite Group Databasebeta

← Group #10853312

Character table — Group #10853312

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222223444444446666666121212121212121244444488888888121212121212121224242424242424242424242424242424448888121212121212121224242424242424244444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11-1
χ1011111111111-1-1-1-111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ1111111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-11
χ1211111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1
χ1311111111111-1-1-1-111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-11
χ1411111111111-1-1-1-111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1111-1
χ1511111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111-1
χ1611111111111-1-1-1-111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ17222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-20000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000220000-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-200000000-2-2-2-222220000000000000000-22000022-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-2222200000000000000002-20000-2-22222-2-2000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-22-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-2222200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-2222200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−3333322000011-1-111-1-133−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-220000-1-11111-1-133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-220000-1-11111-1-1−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-2000011-1-1-1-111−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-2000011-1-1-1-11133−3−3−3−3330000000000000000
χ37222-2-22-2-222222-2-2-2-2-2-2222-2-22222-2-2-2-22-200000000000022-2-222-2-20000000000000000000000000000000000000022-2-22-20000000000
χ38222-2-22-2-222222-2-2-2-2-2-2222-2-22222-2-2-2-22-200000000000022-2-222-2-200000000000000000000000000000000000000-2-222-220000000000
χ39222-2-22-2-2222-2-222-2-2-2-2222-2-22222-2-2-2-2-22000000000000-2-222-2-2220000000000000000000000000000000000000022-2-2-220000000000
χ40222-2-22-2-2222-2-222-2-2-2-2222-2-22222-2-2-2-2-22000000000000-2-222-2-22200000000000000000000000000000000000000-2-2222-20000000000
χ41222-2-22-2-22-2-222-2-222-2-2222-2-2-2-2-2-22222-2200000000000022-2-2-2-22200000000000000000000000000000000000000000000002i−2i2i−2i0000
χ42222-2-22-2-22-2-222-2-222-2-2222-2-2-2-2-2-22222-2200000000000022-2-2-2-2220000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ43222-2-22-2-22-2-2-2-22222-2-2222-2-2-2-2-2-222222-2000000000000-2-22222-2-200000000000000000000000000000000000000000000002i−2i−2i2i0000
χ44222-2-22-2-22-2-2-2-22222-2-2222-2-2-2-2-2-222222-2000000000000-2-22222-2-20000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ4522-22-2-2-2222-200002-2-2-22-2-22222-2-222-2-200000000002i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000002i−2i2i−2i000000002-200
χ4622-22-2-2-2222-200002-2-2-22-2-22222-2-222-2-200000000002i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000−2i2i−2i2i00000000-2200
χ4722-22-2-2-2222-200002-2-2-22-2-22222-2-222-2-20000000000−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000002i−2i2i−2i00000000-2200
χ4822-22-2-2-2222-200002-2-2-22-2-22222-2-222-2-20000000000−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2i2i−2i2i000000002-200
χ4922-2-22-22-222-20000-22222-2-2-2-222-2-2-2-2220000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002i−2i−2i2i002-200000000
χ5022-2-22-22-222-20000-22222-2-2-2-222-2-2-2-2220000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000−2i2i2i−2i00-2200000000
χ5122-2-22-22-222-20000-22222-2-2-2-222-2-2-2-222000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002i−2i−2i2i00-2200000000
χ5222-2-22-22-222-20000-22222-2-2-2-222-2-2-2-222000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000−2i2i2i−2i002-200000000
χ532-2-22-222-22002-22-2002-2-22-22-200000000002-22-2−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−i2i2−i2i22-2002-200−i2i2−i2i2−i2i2−i2i20000000000000000
χ542-2-22-222-22002-22-2002-2-22-22-200000000002-22-2i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200i2−i2i2−i22-2002-200i2−i2i2−i2i2−i2i2−i20000000000000000
χ552-2-22-222-22002-22-2002-2-22-22-20000000000-22-22−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200i2−i2i2−i2-2200-2200i2−i2i2−i2i2−i2i2−i20000000000000000
χ562-2-22-222-22002-22-2002-2-22-22-20000000000-22-22i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−i2i2−i2i2-2200-2200−i2i2−i2i2−i2i2−i2i20000000000000000
χ572-2-22-222-2200-22-22002-2-22-22-200000000002-2-22−i2i2−i2i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200−i2i2i2−i22-200-2200−i2i2−i2i2i2−i2i2−i20000000000000000
χ582-2-22-222-2200-22-22002-2-22-22-200000000002-2-22i2−i2i2−i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200i2−i2−i2i22-200-2200i2−i2i2−i2−i2i2−i2i20000000000000000
χ592-2-22-222-2200-22-22002-2-22-22-20000000000-222-2−i2i2−i2i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200i2−i2−i2i2-22002-200i2−i2i2−i2−i2i2−i2i20000000000000000
χ602-2-22-222-2200-22-22002-2-22-22-20000000000-222-2i2−i2i2−i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200−i2i2i2−i2-22002-200−i2i2−i2i2i2−i2i2−i20000000000000000
χ612-2-22-222-2-1002-22-200-111-11-113−33−33−33−3002-22-2−i2i2−i2i2−i2i2−i2i2-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300−i2i2−i2i2-113−3-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ622-2-22-222-2-1002-22-200-111-11-113−33−33−33−3002-22-2i2−i2i2−i2i2−i2i2−i2-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300i2−i2i2−i2-113−3-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ632-2-22-222-2-1002-22-200-111-11-113−33−33−33−300-22-22−i2i2−i2i2−i2i2−i2i2-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300i2−i2i2−i21-1−331-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ642-2-22-222-2-1002-22-200-111-11-113−33−33−33−300-22-22i2−i2i2−i2i2−i2i2−i2-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300−i2i2−i2i21-1−331-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ652-2-22-222-2-1002-22-200-111-11-11−33−33−33−33002-22-2−i2i2−i2i2−i2i2−i2i2-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700−i2i2−i2i2-11−33-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ662-2-22-222-2-1002-22-200-111-11-11−33−33−33−33002-22-2i2−i2i2−i2i2−i2i2−i2-11-11−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700i2−i2i2−i2-11−33-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ672-2-22-222-2-1002-22-200-111-11-11−33−33−33−3300-22-22−i2i2−i2i2−i2i2−i2i2-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700i2−i2i2−i21-13−31-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.