Finite Group Databasebeta

← Group #10690468

Character table — Group #10690468

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222223444444446666666121212121212121244444488888888121212121212121224242424242424242424242424242424448888121212121212121224242424242424244444444444888822
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ6111111111111111111111111111111111-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ91-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1ii−i−i11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−ii−i11-1-1ii−i−i1-1
χ101-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1ii−i−i11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−ii-1-111−i−iii-11
χ111-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1ii−i−i1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−ii−i11-1-1−i−iii-11
χ121-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1ii−i−i1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iii−ii-1-111ii−i−i1-1
χ131-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1−i−iii11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−ii−i-1-111ii−i−i-11
χ141-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1−i−iii11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−ii11-1-1−i−iii1-1
χ151-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1−i−iii1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−ii−i-1-111−i−iii1-1
χ161-111-1-1-11111-111-1-1-1-1-1111-1-11111-1-1-1-1-1−i−iii1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii−ii11-1-1ii−i−i-11
χ17222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-22222-2000000002222-2-2-2-20000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000220000-2-222-2-222000000000000000000000000
χ19222222222-2-2-22222-2222222222222222-20000-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002222-2-20000000000
χ20222222222-2-2-22222-2222222222222222-20000-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2220000000000
χ21222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-220000200000000-2-2-2-22222000000000000000000000000000000000000000000002-22-2000000
χ22222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-220000200000000-2-2-2-2222200000000000000000000000000000000000000000000-22-22000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-22-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-22222-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ2822222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-22222-200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ2922222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ3022222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−3333322000011-1-111-1-133−3−333−3−30000000000000000
χ31222-22-2-2-222-2-2000022-22-2-22-20000000002-22-20−i2−i2i2i2−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−i2i2−i2i22-2002-200−i2i2−i2i2−i2i2−i2i20000000000000000
χ32222-22-2-2-222-2-2000022-22-2-22-20000000002-22-20i2i2−i2−i2i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200i2−i2i2−i22-2002-200i2−i2i2−i2i2−i2i2−i20000000000000000
χ33222-22-2-2-222-2-2000022-22-2-22-2000000000-22-220−i2−i2i2i2−i2−i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200i2−i2i2−i2-2200-2200i2−i2i2−i2i2−i2i2−i20000000000000000
χ34222-22-2-2-222-2-2000022-22-2-22-2000000000-22-220i2i2−i2−i2i2i2−i2−i22-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−i2i2−i2i2-2200-2200−i2i2−i2i2−i2i2−i2i20000000000000000
χ35222-22-2-2-2-12-2-200002-11-111-1133−3−33−33−302-22-20−i2−i2i2i2−i2−i2i2i2-11-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−i2i2−i2i2-113−3-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ36222-22-2-2-2-12-2-200002-11-111-1133−3−33−33−302-22-20i2i2−i2−i2i2i2−i2−i2-11-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300i2−i2i2−i2-113−3-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ37222-22-2-2-2-12-2-200002-11-111-1133−3−33−33−30-22-220−i2−i2i2i2−i2−i2i2i2-11-113−33−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300i2−i2i2−i21-1−331-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ38222-22-2-2-2-12-2-200002-11-111-1133−3−33−33−30-22-220i2i2−i2−i2i2i2−i2−i2-11-113−33−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−i2i2−i2i21-1−331-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ39222-22-2-2-2-12-2-200002-11-111-11−3−333−33−3302-22-20−i2−i2i2i2−i2−i2i2i2-11-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−i2i2−i2i2-11−33-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ40222-22-2-2-2-12-2-200002-11-111-11−3−333−33−3302-22-20i2i2−i2−i2i2i2−i2−i2-11-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700i2−i2i2−i2-11−33-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ41222-22-2-2-2-12-2-200002-11-111-11−3−333−33−330-22-220−i2−i2i2i2−i2−i2i2i2-11-11−33−33ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700i2−i2i2−i21-13−31-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ42222-22-2-2-2-12-2-200002-11-111-11−3−333−33−330-22-220i2i2−i2−i2i2i2−i2−i2-11-11−33−33−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−i2i2−i2i21-13−31-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ4322-2-2-22-2220002-22-2022-22-2-2-22-22-222-2-20000002−22−22−22−2000000002−22−22−22−22−22−22−22−200000000000000000000002i−2i2i−2i000000−i2i2−i2i200
χ4422-2-2-22-2220002-22-2022-22-2-2-22-22-222-2-20000002−22−22−22−2000000002−22−22−22−22−22−22−22−20000000000000000000000−2i2i−2i2i000000i2−i2i2−i200
χ4522-2-2-22-2220002-22-2022-22-2-2-22-22-222-2-2000000−22−22−22−2200000000−22−22−22−22−22−22−22−2200000000000000000000002i−2i2i−2i000000i2−i2i2−i200
χ4622-2-2-22-2220002-22-2022-22-2-2-22-22-222-2-2000000−22−22−22−2200000000−22−22−22−22−22−22−22−220000000000000000000000−2i2i−2i2i000000−i2i2−i2i200
χ472-222-2-2-22222-2-2-222-2-2-2222-2-2-2-2-2-2222222i2i−2i−2i-20000000022-2-222-2-20000000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ482-222-2-2-22222-2-2-222-2-2-2222-2-2-2-2-2-222222−2i−2i2i2i-20000000022-2-222-2-200000000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ492-222-2-2-222-2-2222-2-22-2-2222-2-22222-2-2-2-220000-200000000-2-22222-2-2000000000000000000000000000000000000002i2i−2i−2i−2i2i0000000000
χ502-222-2-2-222-2-2222-2-22-2-2222-2-22222-2-2-2-220000-200000000-2-22222-2-200000000000000000000000000000000000000−2i−2i2i2i2i−2i0000000000
χ512-222-2-2-222-2-22-2-2222-2-2222-2-2-2-2-2-22222-20000200000000-2-222-2-222000000000000000000000000000000000000000000002-2-22000000
χ522-222-2-2-222-2-22-2-2222-2-2222-2-2-2-2-2-22222-20000200000000-2-222-2-22200000000000000000000000000000000000000000000-222-2000000
χ532-222-2-2-22-122-222-2-2-211-1-1-111-1-1-1-11111-22i2i−2i−2i22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ542-222-2-2-22-122-222-2-2-211-1-1-111-1-1-1-11111-22i2i−2i−2i2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ552-222-2-2-22-122-222-2-2-211-1-1-111-1-1-1-11111-2−2i−2i2i2i22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ562-222-2-2-22-122-222-2-2-211-1-1-111-1-1-1-11111-2−2i−2i2i2i2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ572-222-2-2-22-122-2-2-222-211-1-1-1111111-1-1-1-122i2i−2i−2i-200000000-1-111-1-1113333−3−3−3−3−3−3−3−33333−2i2i0000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000000000
χ582-222-2-2-22-122-2-2-222-211-1-1-1111111-1-1-1-122i2i−2i−2i-200000000-1-111-1-111−3−3−3−333333333−3−3−3−3−2i2i0000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000000000000000
χ592-222-2-2-22-122-2-2-222-211-1-1-1111111-1-1-1-12−2i−2i2i2i-200000000-1-111-1-1113333−3−3−3−3−3−3−3−333332i−2i0000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000000000
χ602-222-2-2-22-122-2-2-222-211-1-1-1111111-1-1-1-12−2i−2i2i2i-200000000-1-111-1-111−3−3−3−333333333−3−3−3−32i−2i0000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000000000000000
χ612-22-2-222-222-220000-2-222-2-2-220000000002i−2i−2i2i0−i2−i2i2i2i2i2−i2−i22-2-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002−2−222i−2i00−2i2i002−22−2−22−220000000000000000
χ622-22-2-222-222-220000-2-222-2-2-220000000002i−2i−2i2i0i2i2−i2−i2−i2−i2i2i22-2-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−222−22i−2i00−2i2i00−22−222−22−20000000000000000
χ632-22-2-222-222-220000-2-222-2-2-22000000000−2i2i2i−2i0−i2−i2i2i2i2i2−i2−i22-2-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−222−2−2i2i002i−2i00−22−222−22−20000000000000000
χ642-22-2-222-222-220000-2-222-2-2-22000000000−2i2i2i−2i0i2i2−i2−i2−i2−i2i2i22-2-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002−2−22−2i2i002i−2i002−22−2−22−220000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.