Finite Group Databasebeta

← Group #10824844

Character table — Group #10824844

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222234444444444446666666121212121212121288888888121212121212121224242424242424242424242424242424244466888812121212121224242424242424242244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ9111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1
χ10111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111
χ11111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ12111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ13111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ14111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ15111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ16111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000002-2-22220000-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-222-2-2-2000022-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000022-2-2220000-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000-2-222-2-200002222-2-2000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2111111111111110000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2112222111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-111113333−3−3−3−33333−3−3−3−32-2-22-1-1000011-1-11133−3−333−3−30000000000000000
χ2622222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-222-2110000-1-111-1-1−3−333−3−3330000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−3−3−3−33333−3−3−3−333332-2-22-1-1000011-1-111−3−333−3−3330000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-222-2110000-1-111-1-133−3−333−3−30000000000000000
χ2922222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-22-2-1-122-2-2-1-11111-1-1-1-111110000000000000000
χ3022222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-22-2211-2-22211-1-1-1-11111-1-1-1-10000000000000000
χ3122222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-22-2-1-1-2-222-1-111111111-1-1-1-10000000000000000
χ3222222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-22-221122-2-211-1-1-1-1-1-1-1-111110000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−3333322-2-2-1-100001111-1-133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-2-222110000-1-1-1-111−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−322-2-2-1-100001111-1-1−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-2-222110000-1-1-1-11133−3−3−3−3330000000000000000
χ3722-2-2-222-222i2i−2i−2i2-22i2i−2i−2i2-222-2-22-2-222-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000002i−2i00002-20000
χ3822-2-2-222-222i2i−2i−2i2-22i2i−2i−2i2-222-2-22-2-222-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000−2i2i0000-220000
χ3922-2-2-222-222i2i−2i−2i-22−2i−2i2i2i-2222-2-22-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000002-200000000002i−2i00
χ4022-2-2-222-222i2i−2i−2i-22−2i−2i2i2i-2222-2-22-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000-220000000000−2i2i00
χ4122-2-2-222-22−2i−2i2i2i2-2−2i−2i2i2i2-222-2-22-2-222-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000002i−2i0000-220000
χ4222-2-2-222-22−2i−2i2i2i2-2−2i−2i2i2i2-222-2-22-2-222-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000−2i2i00002-20000
χ4322-2-2-222-22−2i−2i2i2i-222i2i−2i−2i-2222-2-22-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000002-20000000000−2i2i00
χ4422-2-2-222-22−2i−2i2i2i-222i2i−2i−2i-2222-2-22-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000-2200000000002i−2i00
χ452-22-2-22-2222-22-2222-22-2-2-2-2-2-2-22222222-2-2-2-22i2i−2i−2i2i2i−2i−2i2-22-22-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ462-22-2-22-2222-22-2222-22-2-2-2-2-2-2-22222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2-22-22-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ472-22-2-22-2222-22-2-2-2-22-2222-2-2-2-2222-2-2-2-22222000000002-22-2-22-2200000000000000000000002-22-20000002-22-22-22-20000000000000000
χ482-22-2-22-2222-22-2-2-2-22-2222-2-2-2-2222-2-2-2-22222000000002-22-2-22-220000000000000000000000-22-22000000-22-22-22-220000000000000000
χ492-22-2-22-222-22-2222-22-22-2-2-2-2-2-22222222-2-2-2-22i2i−2i−2i−2i−2i2i2i-22-22-22-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ502-22-2-22-222-22-2222-22-22-2-2-2-2-2-22222222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-22-22-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ512-22-2-22-222-22-22-2-22-22-222-2-2-2-2222-2-2-2-2222200000000-22-222-22-200000000000000000000002-2-220000002-22-2-22-220000000000000000
χ522-22-2-22-222-22-22-2-22-22-222-2-2-2-2222-2-2-2-2222200000000-22-222-22-20000000000000000000000-222-2000000-22-222-22-20000000000000000
χ532-22-2-22-22-12-22-2222-22-2-2-21111-1-1-1-1-1-1-111112i2i−2i−2i2i2i−2i−2i-11-11-11-11−i−iii−i−iii−i−iii−i−iii0000−i3i30000−i3i3−i3i3−i3i33−3−333−3−330000000000000000
χ542-22-2-22-22-12-22-2222-22-2-2-21111-1-1-1-1-1-1-111112i2i−2i−2i2i2i−2i−2i-11-11-11-11−i−iii−i−iii−i−iii−i−iii0000i3−i30000i3−i3i3−i3i3−i3−333−3−333−30000000000000000
χ552-22-2-22-22-12-22-2222-22-2-2-21111-1-1-1-1-1-1-11111−2i−2i2i2i−2i−2i2i2i-11-11-11-11ii−i−iii−i−iii−i−iii−i−i0000−i3i30000−i3i3−i3i3−i3i3−333−3−333−30000000000000000
χ562-22-2-22-22-12-22-2222-22-2-2-21111-1-1-1-1-1-1-11111−2i−2i2i2i−2i−2i2i2i-11-11-11-11ii−i−iii−i−iii−i−iii−i−i0000i3−i30000i3−i3i3−i3i3−i33−3−333−3−330000000000000000
χ572-22-2-22-22-12-22-2-2-2-22-22221111-1-1-11111-1-1-1-100000000-11-111-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000−i3i32-22-2i3−i3−i3i3i3−i3-11-11-11-110000000000000000
χ582-22-2-22-22-12-22-2-2-2-22-22221111-1-1-11111-1-1-1-100000000-11-111-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000i3−i3-22-22−i3i3i3−i3−i3i31-11-11-11-10000000000000000
χ592-22-2-22-22-12-22-2-2-2-22-22221111-1-1-11111-1-1-1-100000000-11-111-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000−i3i3-22-22i3−i3−i3i3i3−i31-11-11-11-10000000000000000
χ602-22-2-22-22-12-22-2-2-2-22-22221111-1-1-11111-1-1-1-100000000-11-111-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000i3−i32-22-2−i3i3i3−i3−i3i3-11-11-11-110000000000000000
χ612-22-2-22-22-1-22-2222-22-22-2-21111-1-1-1-1-1-1-111112i2i−2i−2i−2i−2i2i2i1-11-11-11-1−i−iii−i−iiiii−i−iii−i−i0000−i3i30000−i3i3i3−i3i3−i33−3−33−333−30000000000000000
χ622-22-2-22-22-1-22-2222-22-22-2-21111-1-1-1-1-1-1-111112i2i−2i−2i−2i−2i2i2i1-11-11-11-1−i−iii−i−iiiii−i−iii−i−i0000i3−i30000i3−i3−i3i3−i3i3−333−33−3−330000000000000000
χ632-22-2-22-22-1-22-2222-22-22-2-21111-1-1-1-1-1-1-11111−2i−2i2i2i2i2i−2i−2i1-11-11-11-1ii−i−iii−i−i−i−iii−i−iii0000−i3i30000−i3i3i3−i3i3−i3−333−33−3−330000000000000000
χ642-22-2-22-22-1-22-2222-22-22-2-21111-1-1-1-1-1-1-11111−2i−2i2i2i2i2i−2i−2i1-11-11-11-1ii−i−iii−i−i−i−iii−i−iii0000i3−i30000i3−i3−i3i3−i3i33−3−33−333−30000000000000000
χ652-22-2-22-22-1-22-22-2-22-22-2221111-1-1-11111-1-1-1-1000000001-11-1-11-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−i3i32-2-22i3−i3i3−i3−i3i3-11-111-11-10000000000000000
χ662-22-2-22-22-1-22-22-2-22-22-2221111-1-1-11111-1-1-1-1000000001-11-1-11-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000i3−i3-222-2−i3i3−i3i3i3−i31-11-1-11-110000000000000000
χ672-22-2-22-22-1-22-22-2-22-22-2221111-1-1-11111-1-1-1-1000000001-11-1-11-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−i3i3-222-2i3−i3i3−i3−i3i31-11-1-11-110000000000000000
χ682-22-2-22-22-1-22-22-2-22-22-2221111-1-1-11111-1-1-1-1000000001-11-1-11-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000i3−i32-2-22−i3i3−i3i3i3−i3-11-111-11-10000000000000000
χ692-2-2222-2-222i−2i−2i2i2-22i−2i−2i2i-22-2-2222-2-222-2-2-2-222000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000002-20000002i−2i
χ702-2-2222-2-222i−2i−2i2i2-22i−2i−2i2i-22-2-2222-2-222-2-2-2-222000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000-22000000−2i2i
χ712-2-2222-2-222i−2i−2i2i-22−2i2i2i−2i2-2-2-2222-2-2-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000002-200002i−2i000000
χ722-2-2222-2-222i−2i−2i2i-22−2i2i2i−2i2-2-2-2222-2-2-2-22222-2-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000-220000−2i2i000000
χ732-2-2222-2-22−2i2i2i−2i2-2−2i2i2i−2i-22-2-2222-2-222-2-2-2-22200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000002-2000000−2i2i
χ742-2-2222-2-22−2i2i2i−2i2-2−2i2i2i−2i-22-2-2222-2-222-2-2-2-22200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000-220000002i−2i
χ752-2-2222-2-22−2i2i2i−2i-222i−2i−2i2i2-2-2-2222-2-2-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000002-20000−2i2i000000
χ762-2-2222-2-22−2i2i2i−2i-222i−2i−2i2i2-2-2-2222-2-2-2-22222-2-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000-2200002i−2i000000
χ774444-4-4-4-440000000000004-44-4-44-40000000022−2222−2200000000000022−2222−2222−2222−22000000000000000000000000000000000000000000000000
χ784444-4-4-4-440000000000004-44-4-44-400000000−2222−2222000000000000−2222−2222−2222−2222000000000000000000000000000000000000000000000000
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χ8944-4-4-444-4-24i4i−4i−4i4-44i4i−4i−4i4-4-2-222-222-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
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χ1084-4-44-4-444-20000000000002-2-2222-2−232323−2323−23−23230000−222222−220000000000000000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000000000000

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