Finite Group Databasebeta

← Group #10690174

Character table — Group #10690174

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order1222222222223666666622224444666612121212121212124466668888888812121212242424242424242424242424242424244444444444444444
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
χ911-1-11-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ1011-1-11-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ1111-1-11-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ1211-1-11-1-111-1-1111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ1311-1-11-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ1411-1-11-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ1511-1-11-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ1611-1-11-1-111-1-1111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-200000000222200000000000000000000000000000000
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
χ21222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-100000000111133−3−333−3−333−3−333−3−30000000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-1000000001111−3−333−3−333−3−333−3−3330000000000000000
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
χ25222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122111100000000-1-1-1-133−3−333−3−3−3−333−3−3330000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122111100000000-1-1-1-1−3−333−3−33333−3−333−3−30000000000000000
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
χ312222-2-2-2-222-2-22222-2-2-2-22-22-200002-22-200000000002-22-22−22−22−22−200002−22−22−22−22−22−22−22−20000000000000000
χ322222-2-2-2-222-2-22222-2-2-2-22-22-200002-22-200000000002-22-2−22−22−22−220000−22−22−22−22−22−22−22−220000000000000000
χ332222-2-2-2-222-2-22222-2-2-2-2-22-2200002-22-20000000000-22-222−22−2−22−2200002−22−22−22−2−22−22−22−220000000000000000
χ342222-2-2-2-222-2-22222-2-2-2-2-22-2200002-22-20000000000-22-22−22−222−22−20000−22−22−22−222−22−22−22−20000000000000000
χ352222-2-2-2-222-2-2-1-1-1-111112-22-20000-11-113−33−33−33−300-11-112−22−22−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ362222-2-2-2-222-2-2-1-1-1-111112-22-20000-11-113−33−33−33−300-11-11−22−22−22−223−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ372222-2-2-2-222-2-2-1-1-1-111112-22-20000-11-11−33−33−33−3300-11-112−22−22−22−2−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ382222-2-2-2-222-2-2-1-1-1-111112-22-20000-11-11−33−33−33−3300-11-11−22−22−22−22−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ392222-2-2-2-222-2-2-1-1-1-11111-22-220000-11-113−33−33−33−3001-11-12−22−2−22−22−33−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ402222-2-2-2-222-2-2-1-1-1-11111-22-220000-11-113−33−33−33−3001-11-1−22−222−22−2−33−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ412222-2-2-2-222-2-2-1-1-1-11111-22-220000-11-11−33−33−33−33001-11-12−22−2−22−223−33−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ422222-2-2-2-222-2-2-1-1-1-11111-22-220000-11-11−33−33−33−33001-11-1−22−222−22−23−33−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ4322-2-22-2-222-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-22222-2222-2-200000000-2-22200000000000000000000000000000000
χ4422-2-22-2-222-2-2222-2-2-2-222-2-222-2-22222-2-2-2-2-2-222222-2-2-2220000000022-2-200000000000000000000000000000000
χ4522-2-22-2-222-2-22-1-11111-1-122-2-222-2-2-1-111-1-1-1-111112-2-1-1112i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ4622-2-22-2-222-2-22-1-11111-1-122-2-222-2-2-1-111-1-1-1-111112-2-1-111−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ4722-2-22-2-222-2-22-1-11111-1-122-2-2-2-222-1-1111111-1-1-1-1-22-1-1110000000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ4822-2-22-2-222-2-22-1-11111-1-122-2-2-2-222-1-1111111-1-1-1-1-22-1-1110000000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ4922-2-22-2-222-2-22-1-11111-1-1-2-22222-2-2-1-111-1-1-1-11111-2211-1-12i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ5022-2-22-2-222-2-22-1-11111-1-1-2-22222-2-2-1-111-1-1-1-11111-2211-1-1−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ5122-2-22-2-222-2-22-1-11111-1-1-2-222-2-222-1-1111111-1-1-1-12-211-1-100000000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ5222-2-22-2-222-2-22-1-11111-1-1-2-222-2-222-1-1111111-1-1-1-12-211-1-100000000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ5322-2-22-2-22-222-222-2-2-2-22200002-2-22-2-22222-2-2-2-22200000000000000000000000000000000002i−2i−2i2i000000000000
χ5422-2-22-2-22-222-222-2-2-2-22200002-2-22-2-22222-2-2-2-2220000000000000000000000000000000000−2i2i2i−2i000000000000
χ5522-2-22-2-22-222-222-2-2-2-2220000-222-2-2-222-2-22222-2-2000000000000000000000000000000000000002i−2i−2i2i00000000
χ5622-2-22-2-22-222-222-2-2-2-2220000-222-2-2-222-2-22222-2-200000000000000000000000000000000000000−2i2i2i−2i00000000
χ5722-2-2-222-22-22-222-2-222-2-22-2-2200002-2-2200000000002-2-22−i2i2i2−i2−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ5822-2-2-222-22-22-222-2-222-2-22-2-2200002-2-2200000000002-2-22i2−i2−i2i2i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5922-2-2-222-22-22-222-2-222-2-2-222-200002-2-220000000000-222-2−i2i2i2−i2i2−i2−i2i20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ6022-2-2-222-22-22-222-2-222-2-2-222-200002-2-220000000000-222-2i2−i2−i2i2−i2i2i2−i20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ6122-2-2-222-22-22-2-1-111-1-1112-2-220000-111-13−33−3−33−3300-111-1−i2i2i2−i2−i2i2i2−i23−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ6222-2-2-222-22-22-2-1-111-1-1112-2-220000-111-13−33−3−33−3300-111-1i2−i2−i2i2i2−i2−i2i23−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ6322-2-2-222-22-22-2-1-111-1-1112-2-220000-111-1−33−333−33−300-111-1−i2i2i2−i2−i2i2i2−i2−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6422-2-2-222-22-22-2-1-111-1-1112-2-220000-111-1−33−333−33−300-111-1i2−i2−i2i2i2−i2−i2i2−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ6522-2-2-222-22-22-2-1-111-1-111-222-20000-111-13−33−3−33−33001-1-11−i2i2i2−i2i2−i2−i2i2−333−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ6622-2-2-222-22-22-2-1-111-1-111-222-20000-111-13−33−3−33−33001-1-11i2−i2−i2i2−i2i2i2−i2−333−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ6722-2-2-222-22-22-2-1-111-1-111-222-20000-111-1−33−333−33−3001-1-11−i2i2i2−i2i2−i2−i2i23−3−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ6822-2-2-222-22-22-2-1-111-1-111-222-20000-111-1−33−333−33−3001-1-11i2−i2−i2i2−i2i2i2−i23−3−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
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
χ714444-4-4-4-4-4-4444444-4-4-4-400000000-44-440000000000000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-4-444-2-2-2-22222000000002-22-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-4-444-2-2-2-22222000000002-22-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ7444-4-44-4-44-444-4-2-22222-2-200004-4-4422-2-2-2-22222-2-200000000000000000000000000000000000000000000000000
χ7544-4-44-4-44-444-4-2-22222-2-20000-444-422-2-222-2-2-2-22200000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-44-4444-4-444-4-400000000-444-40000000000000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-44-44-2-222-2-222000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-44-44-2-222-2-222000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ794-44-444-4-400004-44-44-44-40000000000000000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ804-44-444-4-400004-44-44-44-4000000000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ814-44-4-4-44400004-44-4-44-44000000000000000000000000000000000000000000000000000000000000002-22-20000
χ824-44-4-4-44400004-44-4-44-4400000000000000000000000000000000000000000000000000000000000000-22-220000
χ834-4-444-44-400004-4-44-444-40000000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ844-4-444-44-400004-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ854-4-44-44-4400004-4-444-4-44000000000000000000000000000000000000000000000000000000000000002-2-220000
χ864-4-44-44-4400004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000-222-20000
χ878-88-888-8-80000-44-44-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-8-8880000-44-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-888-88-80000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-880000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000

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