Finite Group Databasebeta

← Group #10824505

Character table — Group #10824505

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222223444444444444666666612121212121212128888888812121212121212122424242424242424242424242424242444448888121212121212121224242424242424242222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1
χ1011111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ1111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1411111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111
χ1611111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-1
χ17222222222-2-22222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-2000022-2-222-2-2000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000002-2-22000022-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000-222-20000-2-22222-2-2000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-22-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-22-22-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-22-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-22-2222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-111113333−3−3−3−33333−3−3−3−322-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ3022222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2-222000011-1-111-1-1−3−333−3−3330000000000000000
χ3122222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−3−3−3−33333−3−3−3−3333322-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ3222222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2-222000011-1-111-1-133−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-2-220000-1-11111-1-133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-222-2000011-1-1-1-111−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-2-220000-1-11111-1-1−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-222-2000011-1-1-1-11133−3−3−3−3330000000000000000
χ3722-222-2-2-222-22i2i−2i−2i2i2i−2i−2i2-2222-2-2-2-222-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000002-2002i−2i0000000000
χ3822-222-2-2-222-22i2i−2i−2i2i2i−2i−2i2-2222-2-2-2-222-2-222-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000-2200−2i2i0000000000
χ3922-222-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-2222-2-2-2-222-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000002-200−2i2i0000000000
χ4022-222-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-2222-2-2-2-222-2-222-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000-22002i−2i0000000000
χ4122-222-2-2-22-222i2i−2i−2i−2i−2i2i2i-22222-2-2-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000002-200000000002i−2i
χ4222-222-2-2-22-222i2i−2i−2i−2i−2i2i2i-22222-2-2-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000-220000000000−2i2i
χ4322-222-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22222-2-2-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000002-20000000000−2i2i
χ4422-222-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22222-2-2-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000-2200000000002i−2i
χ452-222-22-2-222-22i−2i2i−2i2i−2i2i−2i-222-2-222-2-222-2-2-2-222000000002i−2i2i−2i2i−2i2i−2i000000000000000000002-22i−2i000000002-22-22i−2i2i−2i0000000000000000
χ462-222-22-2-222-22i−2i2i−2i2i−2i2i−2i-222-2-222-2-222-2-2-2-222000000002i−2i2i−2i2i−2i2i−2i00000000000000000000-22−2i2i00000000-22-22−2i2i−2i2i0000000000000000
χ472-222-22-2-222-2−2i2i−2i2i−2i2i−2i2i-222-2-222-2-222-2-2-2-22200000000−2i2i−2i2i−2i2i−2i2i000000000000000000002-2−2i2i000000002-22-2−2i2i−2i2i0000000000000000
χ482-222-22-2-222-2−2i2i−2i2i−2i2i−2i2i-222-2-222-2-222-2-2-2-22200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000-222i−2i00000000-22-222i−2i2i−2i0000000000000000
χ492-222-22-2-22-222i−2i2i−2i−2i2i−2i2i2-22-2-222-2-2-2-22222-2-222-2-22i2i−2i−2i2i−2i2i−2i−2i2i−2i2i22-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ502-222-22-2-22-222i−2i2i−2i−2i2i−2i2i2-22-2-222-2-2-2-22222-2-2-2-222−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ512-222-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-22-2-222-2-2-2-22222-2-222-2-2−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ522-222-22-2-22-22−2i2i−2i2i2i−2i2i−2i2-22-2-222-2-2-2-22222-2-2-2-2222i2i−2i−2i−2i2i−2i2i2i−2i2i−2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ532-222-22-2-2-12-22i−2i2i−2i2i−2i2i−2i-22-111-1-111-1-11111-1-100000000−ii−ii−ii−ii33−3−3−3−333i3i3−i3−i3−i3−i3i3i300002-22i−2i3−33−3−i3i3−i3i3-11-11−ii−ii0000000000000000
χ542-222-22-2-2-12-22i−2i2i−2i2i−2i2i−2i-22-111-1-111-1-11111-1-100000000−ii−ii−ii−ii33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000-22−2i2i−33−33i3−i3i3−i31-11-1i−ii−i0000000000000000
χ552-222-22-2-2-12-22i−2i2i−2i2i−2i2i−2i-22-111-1-111-1-11111-1-100000000−ii−ii−ii−ii−3−33333−3−3−i3−i3i3i3i3i3−i3−i300002-22i−2i−33−33i3−i3i3−i3-11-11−ii−ii0000000000000000
χ562-222-22-2-2-12-22i−2i2i−2i2i−2i2i−2i-22-111-1-111-1-11111-1-100000000−ii−ii−ii−ii−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000-22−2i2i3−33−3−i3i3−i3i31-11-1i−ii−i0000000000000000
χ572-222-22-2-2-12-2−2i2i−2i2i−2i2i−2i2i-22-111-1-111-1-11111-1-100000000i−ii−ii−ii−i33−3−3−3−333−i3−i3i3i3i3i3−i3−i300002-2−2i2i3−33−3i3−i3i3−i3-11-11i−ii−i0000000000000000
χ582-222-22-2-2-12-2−2i2i−2i2i−2i2i−2i2i-22-111-1-111-1-11111-1-100000000i−ii−ii−ii−i33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000-222i−2i−33−33−i3i3−i3i31-11-1−ii−ii0000000000000000
χ592-222-22-2-2-12-2−2i2i−2i2i−2i2i−2i2i-22-111-1-111-1-11111-1-100000000i−ii−ii−ii−i−3−33333−3−3i3i3−i3−i3−i3−i3i3i300002-2−2i2i−33−33−i3i3−i3i3-11-11i−ii−i0000000000000000
χ602-222-22-2-2-12-2−2i2i−2i2i−2i2i−2i2i-22-111-1-111-1-11111-1-100000000i−ii−ii−ii−i−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000-222i−2i3−33−3i3−i3i3−i31-11-1−ii−ii0000000000000000
χ612-222-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-2-111-1-11111-1-1-1-11122-2-22i2i−2i−2i−ii−iii−ii−i-1-111-1-111−i−iii−i−iii000000003−3−33−i3i3i3−i3−333−3−i3i3i3−i30000000000000000
χ622-222-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-2-111-1-11111-1-1-1-11122-2-22i2i−2i−2i−ii−iii−ii−i-1-111-1-111−i−iii−i−iii00000000−333−3i3−i3−i3i33−3−33i3−i3−i3i30000000000000000
χ632-222-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-2-111-1-11111-1-1-1-111-2-222−2i−2i2i2i−ii−iii−ii−i11-1-111-1-1ii−i−iii−i−i000000003−3−33−i3i3i3−i33−3−33i3−i3−i3i30000000000000000
χ642-222-22-2-2-1-222i−2i2i−2i−2i2i−2i2i2-2-111-1-11111-1-1-1-111-2-222−2i−2i2i2i−ii−iii−ii−i11-1-111-1-1ii−i−iii−i−i00000000−333−3i3−i3−i3i3−333−3−i3i3i3−i30000000000000000
χ652-222-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-2-111-1-11111-1-1-1-11122-2-2−2i−2i2i2ii−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i000000003−3−33i3−i3−i3i3−333−3i3−i3−i3i30000000000000000
χ662-222-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-2-111-1-11111-1-1-1-11122-2-2−2i−2i2i2ii−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i00000000−333−3−i3i3i3−i33−3−33−i3i3i3−i30000000000000000
χ672-222-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-2-111-1-11111-1-1-1-111-2-2222i2i−2i−2ii−ii−i−ii−ii11-1-111-1-1−i−iii−i−iii000000003−3−33i3−i3−i3i33−3−33−i3i3i3−i30000000000000000
χ682-222-22-2-2-1-22−2i2i−2i2i2i−2i2i−2i2-2-111-1-11111-1-1-1-111-2-2222i2i−2i−2ii−ii−i−ii−ii11-1-111-1-1−i−iii−i−iii00000000−333−3−i3i3i3−i3−333−3i3−i3−i3i30000000000000000
χ692-2-22-2-2222222-2-222-2-22-2-22-2-2-2-2222222-2-2-2-2000000002-2-222-2-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ702-2-22-2-2222222-2-222-2-22-2-22-2-2-2-2222222-2-2-2-2000000002-2-222-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ712-2-22-2-222222-222-2-222-2-2-22-2-2-2-2222222-2-2-2-200000000-222-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ722-2-22-2-222222-222-2-222-2-2-22-2-2-2-2222222-2-2-2-200000000-222-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ732-2-22-2-2222-2-22-2-22-222-2222-2-2-2-222-2-2-2-22222000000002-2-22-222-200000000000000000000000000000000000000000000002-200002-200
χ742-2-22-2-2222-2-22-2-22-222-2222-2-2-2-222-2-2-2-22222000000002-2-22-222-20000000000000000000000000000000000000000000000-220000-2200
χ752-2-22-2-2222-2-2-222-22-2-22222-2-2-2-222-2-2-2-2222200000000-222-22-2-2200000000000000000000000000000000000000000000002-20000-2200
χ762-2-22-2-2222-2-2-222-22-2-22222-2-2-2-222-2-2-2-2222200000000-222-22-2-220000000000000000000000000000000000000000000000-2200002-200
χ77444-4-4-4-444000000000000-44-44-44-400000000−2i22i2−2i22i2000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ78444-4-4-4-444000000000000-44-44-44-4000000002i2−2i22i2−2i20000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ79444-4-4-4-44-20000000000002-22-22-2223−2323−2323−2323−23−2i22i2−2i22i20000000000002ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000000000000000
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χ8944-4-4-444-4-20000000000002-222-22-223−23−232323−23−23230000−2i22i2−2i22i200000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000000000000000
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χ1034-4-4-444-444000000000000-4-44-444-400000000000022−22−2222000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ1044-4-4-444-444000000000000-4-44-444-4000000000000−222222−220000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ1054-4-4-444-44-200000000000022-22-2-2223−2323−23−2323−2323000022−22−222200000000000000002ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000000000000000
χ1064-4-4-444-44-200000000000022-22-2-2223−2323−23−2323−23230000−222222−220000000000000000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000000000000
χ1074-4-4-444-44-200000000000022-22-2-22−2323−232323−2323−23000022−22−222200000000000000002ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000000000000
χ1084-4-4-444-44-200000000000022-22-2-22−2323−232323−2323−230000−222222−220000000000000000−2ζ13+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.