Finite Group Databasebeta

← Group #11777892

Character table — Group #11777892

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111111112222222222222222222244444444444444448888888888888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636367272
order12224444334444666666121212121212121236661212121212121212121212122466666666121212121212121212121212888888882424242424242424242424242424242444881212121224242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-111111111-1-1-1-111-1-1-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-111111111-1-1-1-111-1-1-1-1-1-1i−ii−i-1-111ii−i−iii−i−i-1-1-1-11111-11i−i-1-111ii−i−i−i−iii−ii
χ111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-111111111-1-1-1-111-1-1-1-1-1-1−ii−ii11-1-1−i−iii−i−iii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii−ii
χ121111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-111111111-1-1-1-111-1-1-1-1-1-1−ii−ii-1-111−i−iii−i−iii-1-1-1-11111-11−ii-1-111−i−iiiii−i−ii−i
χ131111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-11111i−ii−i11-1-1ii−i−iii−i−i1111-1-1-1-1-11−ii-1-111−i−iiiii−i−i−ii
χ141111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-11111i−ii−i-1-111ii−i−iii−i−i-1-1-1-111111-1−ii11-1-1−i−iii−i−iiii−i
χ151111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-11111−ii−ii11-1-1−i−iii−i−iii1111-1-1-1-1-11i−i-1-111ii−i−i−i−iiii−i
χ161111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-11111−ii−ii-1-111−i−iii−i−iii-1-1-1-111111-1i−i11-1-1ii−i−iii−i−i−ii
χ172222222222-2-2-2-2222222222222222222-2-2-2-2-2-22222-2-200000000000000-2-2-2-2000022-2-200002222-2-2-2-200000000000000000000000000
χ182222222222-2-2-2-2222222222222222222-2-2-2-2-2-22222-2-200000000000000-2-2-2-20000-2-2220000-2-2-2-2222200000000000000000000000000
χ19222222222-12222222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-12200-1-1-1-10000000000
χ20222222222-12222222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111-2-20011110000000000
χ21222222222-12222222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111-2-211-1-1-1-111110000222200000000-1-1-1-1-1-1-1-1-2-20011110000000000
χ22222222222-12222222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111-2-211-1-1-1-111110000-2-2-2-200000000111111112200-1-1-1-10000000000
χ2322222222-122222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000220000-1-1-1-1000000
χ2422222222-122222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000-2-200001111000000
χ2522222222-122222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-2-211-2-2111111-2-2-1-1-1-1111122220000-1-1-1-1-1-1-1-10000000000-2-200001111000000
χ2622222222-122222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-2-211-2-2111111-2-2-1-1-1-11111-2-2-2-20000111111110000000000220000-1-1-1-1000000
χ2722222222-12-2-2-2-2-1-1-12222222-1-1-1-1-1-1-1-11111-2-2-1-1-1-1-2-200−i3i300−i3−i3i3i3−i3i3001111−i3−i3i3i322-2-20000-1-1-1-111110000000000000000−i3i3−i3i3000000
χ2822222222-12-2-2-2-2-1-1-12222222-1-1-1-1-1-1-1-11111-2-2-1-1-1-1-2-200−i3i300−i3−i3i3i3−i3i3001111−i3−i3i3i3-2-22200001111-1-1-1-10000000000000000i3−i3i3−i3000000
χ2922222222-12-2-2-2-2-1-1-12222222-1-1-1-1-1-1-1-11111-2-2-1-1-1-1-2-200i3−i300i3i3−i3−i3i3−i3001111i3i3−i3−i322-2-20000-1-1-1-111110000000000000000i3−i3i3−i3000000
χ3022222222-12-2-2-2-2-1-1-12222222-1-1-1-1-1-1-1-11111-2-2-1-1-1-1-2-200i3−i300i3i3−i3−i3i3−i3001111i3i3−i3−i3-2-22200001111-1-1-1-10000000000000000−i3i3−i3i3000000
χ312222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-200000000000000-2-22200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ322222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-200000000000000-2-2220000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ332222-2-2-2-22-122-2-2222-1-1-11111-2-2-2-2-1-1-1-122-2-2111111-1-12-222-1-1-1-1-1-1-2-211-1-1111111000022-2-200000000-1-1-1-111112-200-1-1110000000000
χ342222-2-2-2-22-122-2-2222-1-1-11111-2-2-2-2-1-1-1-122-2-2111111-1-12-222-1-1-1-1-1-1-2-211-1-11111110000-2-222000000001111-1-1-1-1-220011-1-10000000000
χ352222-2-2-2-22-122-2-2222-1-1-11111-2-2-2-2-1-1-1-122-2-2111111-1-1-22-2-211111122-1-1-1-111-1-1-1-1000022-2-200000000-1-1-1-11111-220011-1-10000000000
χ362222-2-2-2-22-122-2-2222-1-1-11111-2-2-2-2-1-1-1-122-2-2111111-1-1-22-2-211111122-1-1-1-111-1-1-1-10000-2-222000000001111-1-1-1-12-200-1-1110000000000
χ372222-2-2-2-2-1222-2-2-1-1-1222-2-2-2-21111-1-1-1-1-1-111-2-21111222-2-1-122-1-1-1-111-2-2-1-11111112i−2i2i−2i0000−i−iii−i−iii00000000002i−2i0000−i−iii000000
χ382222-2-2-2-2-1222-2-2-1-1-1222-2-2-2-21111-1-1-1-1-1-111-2-21111222-2-1-122-1-1-1-111-2-2-1-1111111−2i2i−2i2i0000ii−i−iii−i−i0000000000−2i2i0000ii−i−i000000
χ392222-2-2-2-2-1222-2-2-1-1-1222-2-2-2-21111-1-1-1-1-1-111-2-2111122-2211-2-21111-1-122-1-111-1-1-1-12i−2i2i−2i0000−i−iii−i−iii0000000000−2i2i0000ii−i−i000000
χ402222-2-2-2-2-1222-2-2-1-1-1222-2-2-2-21111-1-1-1-1-1-111-2-2111122-2211-2-21111-1-122-1-111-1-1-1-1−2i2i−2i2i0000ii−i−iii−i−i00000000002i−2i0000−i−iii000000
χ412222-2-2-2-2-12-2-222-1-1-1222-2-2-2-21111-1-1-1-111-1-1221111-2-200−i3i300−i3−i3i3i3i3−i30011-1-1i3i3−i3−i32i−2i−2i2i0000−i−iiiii−i−i00000000000000003−3−33000000
χ422222-2-2-2-2-12-2-222-1-1-1222-2-2-2-21111-1-1-1-111-1-1221111-2-200−i3i300−i3−i3i3i3i3−i30011-1-1i3i3−i3−i3−2i2i2i−2i0000ii−i−i−i−iii0000000000000000−333−3000000
χ432222-2-2-2-2-12-2-222-1-1-1222-2-2-2-21111-1-1-1-111-1-1221111-2-200i3−i300i3i3−i3−i3−i3i30011-1-1−i3−i3i3i32i−2i−2i2i0000−i−iiiii−i−i0000000000000000−333−3000000
χ442222-2-2-2-2-12-2-222-1-1-1222-2-2-2-21111-1-1-1-111-1-1221111-2-200i3−i300i3i3−i3−i3−i3i30011-1-1−i3−i3i3i3−2i2i2i−2i0000ii−i−i−i−iii00000000000000003−3−33000000
χ452-22-22i−2i2i−2i222-22i−2i2-2-2-22-22i2i−2i−2i2i−2i2i−2i22-2-22-22i−2i2i−2i2i2i−2i−2i2-2000000000000002-22i−2i00000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ462-22-22i−2i2i−2i222-22i−2i2-2-2-22-22i2i−2i−2i2i−2i2i−2i22-2-22-22i−2i2i−2i2i2i−2i−2i2-2000000000000002-22i−2i0000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ472-22-22i−2i2i−2i22-22−2i2i2-2-2-22-22i2i−2i−2i2i−2i2i−2i22-2-2-22−2i2i−2i2i2i2i−2i−2i-2200000000000000-22−2i2i000000002i−2i2-2000000002i2i−2i−2i22-2-2000000000000000000
χ482-22-22i−2i2i−2i22-22−2i2i2-2-2-22-22i2i−2i−2i2i−2i2i−2i22-2-2-22−2i2i−2i2i2i2i−2i−2i-2200000000000000-22−2i2i00000000−2i2i-2200000000−2i−2i2i2i-2-222000000000000000000
χ492-22-22i−2i2i−2i2-1-22−2i2i2-2-21-11−i−iii2i−2i2i−2i-1-111-22−2i2ii−i−i−iii1-10000−i3i3−i3i3−i3i3003−31-1i−i3−33−300002i−2i2-200000000−i−iii-1-11100003−3−i3i30000000000
χ502-22-22i−2i2i−2i2-1-22−2i2i2-2-21-11−i−iii2i−2i2i−2i-1-111-22−2i2ii−i−i−iii1-10000−i3i3−i3i3−i3i3003−31-1i−i3−33−30000−2i2i-2200000000ii−i−i11-1-10000−33i3−i30000000000
χ512-22-22i−2i2i−2i2-1-22−2i2i2-2-21-11−i−iii2i−2i2i−2i-1-111-22−2i2ii−i−i−iii1-10000i3−i3i3−i3i3−i300−331-1i−i−33−3300002i−2i2-200000000−i−iii-1-1110000−33i3−i30000000000
χ522-22-22i−2i2i−2i2-1-22−2i2i2-2-21-11−i−iii2i−2i2i−2i-1-111-22−2i2ii−i−i−iii1-10000i3−i3i3−i3i3−i300−331-1i−i−33−330000−2i2i-2200000000ii−i−i11-1-100003−3−i3i30000000000
χ532-22-2−2i2i−2i2i222-2−2i2i2-2-2-22-2−2i−2i2i2i−2i2i−2i2i22-2-22-2−2i2i−2i2i−2i−2i2i2i2-2000000000000002-2−2i2i0000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ542-22-2−2i2i−2i2i222-2−2i2i2-2-2-22-2−2i−2i2i2i−2i2i−2i2i22-2-22-2−2i2i−2i2i−2i−2i2i2i2-2000000000000002-2−2i2i00000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ552-22-2−2i2i−2i2i22-222i−2i2-2-2-22-2−2i−2i2i2i−2i2i−2i2i22-2-2-222i−2i2i−2i−2i−2i2i2i-2200000000000000-222i−2i000000002i−2i-22000000002i2i−2i−2i-2-222000000000000000000
χ562-22-2−2i2i−2i2i22-222i−2i2-2-2-22-2−2i−2i2i2i−2i2i−2i2i22-2-2-222i−2i2i−2i−2i−2i2i2i-2200000000000000-222i−2i00000000−2i2i2-200000000−2i−2i2i2i22-2-2000000000000000000
χ572-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11ii−i−i−2i2i−2i2i-1-111-222i−2i−iiii−i−i1-10000−i3i3−i3i3−i3i300−331-1−ii−33−3300002i−2i-2200000000−i−iii11-1-100003−3i3−i30000000000
χ582-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11ii−i−i−2i2i−2i2i-1-111-222i−2i−iiii−i−i1-10000−i3i3−i3i3−i3i300−331-1−ii−33−330000−2i2i2-200000000ii−i−i-1-1110000−33−i3i30000000000
χ592-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11ii−i−i−2i2i−2i2i-1-111-222i−2i−iiii−i−i1-10000i3−i3i3−i3i3−i3003−31-1−ii3−33−300002i−2i-2200000000−i−iii11-1-10000−33−i3i30000000000
χ602-22-2−2i2i−2i2i2-1-222i−2i2-2-21-11ii−i−i−2i2i−2i2i-1-111-222i−2i−iiii−i−i1-10000i3−i3i3−i3i3−i3003−31-1−ii3−33−30000−2i2i2-200000000ii−i−i-1-11100003−3i3−i30000000000
χ61444444444-2-4-4-4-4444-2-2-2-2-2-2-24444-2-2-2-2-4-4-4-422-2-2-2-2220000000000000022220000000000000000000000000000000000000000000000
χ6244444444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-21111-2-244-2-2-2-21111-2-2-2-211111111000000000000000000000000000000000000000000
χ6344444444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-21111-2-2-4-42222-1-1-1-122221111-1-1-1-1000000000000000000000000000000000000000000
χ6444444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2111122222211112200−2i32i300i3i3−i3−i3−2i32i300-1-1-1-1i3i3−i3−i3000000000000000000000000000000000000000000
χ6544444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21111222222111122002i3−2i300−i3−i3i3i32i3−2i300-1-1-1-1−i3−i3i3i3000000000000000000000000000000000000000000
χ664444-4-4-4-44-2-4-444444-2-2-22222-4-4-4-4-2-2-2-2-4-444-2-22222220000000000000022-2-20000000000000000000000000000000000000000000000
χ674444-4-4-4-4-2-244-4-4-2-2-2-2-2-2222222221111-2-22222-1-1-1-1-2-24-4-2-2-2-21111222211-1-1-1-1-1-1000000000000000000000000000000000000000000
χ684444-4-4-4-4-2-244-4-4-2-2-2-2-2-2222222221111-2-22222-1-1-1-1-2-2-442222-1-1-1-1-2-2-2-211-1-11111000000000000000000000000000000000000000000
χ694444-4-4-4-4-2-2-4-444-2-2-2-2-2-222222222111122-2-2-2-2-1-1-1-12200−2i32i300i3i3−i3−i32i3−2i300-1-111−i3−i3i3i3000000000000000000000000000000000000000000
χ704444-4-4-4-4-2-2-4-444-2-2-2-2-2-222222222111122-2-2-2-2-1-1-1-122002i3−2i300−i3−i3i3i3−2i32i300-1-111i3i3−i3−i3000000000000000000000000000000000000000000
χ7144-4-444-4-4440000-4-444-4-44-44-444-4-44-4-440000004-44-4000000000000000000000000000000000000000000000000000000000000000000
χ7244-4-444-4-44-20000-4-44-222-22-2244-4-4-222-2000000-22-2200000000000000000000000000000000000000006−66−66−66−6000000000000000000
χ7344-4-444-4-44-20000-4-44-222-22-2244-4-4-222-2000000-22-220000000000000000000000000000000000000000−66−66−66−66000000000000000000
χ7444-4-444-4-4-24000022-24-4-44-44-4-2-222-222-2000000-22-2200000000000000000000000000000000000023−2323−2300000000000000000000000000
χ7544-4-444-4-4-24000022-24-4-44-44-4-2-222-222-2000000-22-22000000000000000000000000000000000000−2323−232300000000000000000000000000
χ7644-4-4-4-444440000-4-444-4-4-44-44-4-4444-4-44000000-44-44000000000000000000000000000000000000000000000000000000000000000000
χ7744-4-4-4-4444-20000-4-44-2222-22-2-4-444-222-20000002-22-200000000000000000000000000000000000000006−66−6−66−66000000000000000000
χ7844-4-4-4-4444-20000-4-44-2222-22-2-4-444-222-20000002-22-20000000000000000000000000000000000000000−66−666−66−6000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.