Finite Group Databasebeta

← Group #10824410

Character table — Group #10824410

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222223444444444444666666612121212121212124444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ9111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ12111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ14111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1
χ15111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ16111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ172222222222222-2-2-2-2-2-2-2-222222222222222222-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222222222222222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
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
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-11111-1-1-1-111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2622222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-11111-1-1-1-111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2922222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-111112222-2-2-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ3022222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111-2-2-2-222221111-1-1-1-11111-1-1-1-10000000000000000
χ3122222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-111111111-2-222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1111122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ3222222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-111111111-2-222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-11111-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3722-2-222-2-222i2i−2i−2i2-22i2i−2i−2i2-222-2-2-22-22i2i2i2i−2i−2i−2i−2i00000000000000000000000022-2-22i2i−2i−2i002-2002i−2i000000002-22-22i−2i2i−2i0000000000000000
χ3822-2-222-2-222i2i−2i−2i2-22i2i−2i−2i2-222-2-2-22-22i2i2i2i−2i−2i−2i−2i00000000000000000000000022-2-22i2i−2i−2i00-2200−2i2i00000000-22-22−2i2i−2i2i0000000000000000
χ3922-2-222-2-222i2i−2i−2i-22−2i−2i2i2i-2222-2-2-22-22i2i2i2i−2i−2i−2i−2i000000000000000000000000-2-222−2i−2i2i2i2-2002i−2i002-22-22i−2i2i−2i000000000000000000000000
χ4022-2-222-2-222i2i−2i−2i-22−2i−2i2i2i-2222-2-2-22-22i2i2i2i−2i−2i−2i−2i000000000000000000000000-2-222−2i−2i2i2i-2200−2i2i00-22-22−2i2i−2i2i000000000000000000000000
χ4122-2-222-2-22−2i−2i2i2i2-2−2i−2i2i2i2-222-2-2-22-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000022-2-2−2i−2i2i2i002-200−2i2i000000002-22-2−2i2i−2i2i0000000000000000
χ4222-2-222-2-22−2i−2i2i2i2-2−2i−2i2i2i2-222-2-2-22-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000022-2-2−2i−2i2i2i00-22002i−2i00000000-22-222i−2i2i−2i0000000000000000
χ4322-2-222-2-22−2i−2i2i2i-222i2i−2i−2i-2222-2-2-22-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000-2-2222i2i−2i−2i2-200−2i2i002-22-2−2i2i−2i2i000000000000000000000000
χ4422-2-222-2-22−2i−2i2i2i-222i2i−2i−2i-2222-2-2-22-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000-2-2222i2i−2i−2i-22002i−2i00-22-222i−2i2i−2i000000000000000000000000
χ4522-2-222-2-2-12i2i−2i−2i2-22i2i−2i−2i2-2-1-1111-11−i−i−i−iiiii00000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3-1-111−i−iii002-2002i−2i−i3i3i3−i33−3−33-11-11−ii−ii0000000000000000
χ4622-2-222-2-2-12i2i−2i−2i2-22i2i−2i−2i2-2-1-1111-11−i−i−i−iiiii00000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3-1-111−i−iii00-2200−2i2ii3−i3−i3i3−333−31-11-1i−ii−i0000000000000000
χ4722-2-222-2-2-12i2i−2i−2i2-22i2i−2i−2i2-2-1-1111-11−i−i−i−iiiii00000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333-1-111−i−iii002-2002i−2ii3−i3−i3i3−333−3-11-11−ii−ii0000000000000000
χ4822-2-222-2-2-12i2i−2i−2i2-22i2i−2i−2i2-2-1-1111-11−i−i−i−iiiii00000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333-1-111−i−iii00-2200−2i2i−i3i3i3−i33−3−331-11-1i−ii−i0000000000000000
χ4922-2-222-2-2-12i2i−2i−2i-22−2i−2i2i2i-22-1-1111-11−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−33311-1-1ii−i−i2-2002i−2i00-11-11−ii−ii−i3i3i3−i33−3−330000000000000000
χ5022-2-222-2-2-12i2i−2i−2i-22−2i−2i2i2i-22-1-1111-11−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−33311-1-1ii−i−i-2200−2i2i001-11-1i−ii−ii3−i3−i3i3−333−30000000000000000
χ5122-2-222-2-2-12i2i−2i−2i-22−2i−2i2i2i-22-1-1111-11−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−311-1-1ii−i−i2-2002i−2i00-11-11−ii−iii3−i3−i3i3−333−30000000000000000
χ5222-2-222-2-2-12i2i−2i−2i-22−2i−2i2i2i-22-1-1111-11−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−311-1-1ii−i−i-2200−2i2i001-11-1i−ii−i−i3i3i3−i33−3−330000000000000000
χ5322-2-222-2-2-1−2i−2i2i2i2-2−2i−2i2i2i2-2-1-1111-11iiii−i−i−i−i00000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333-1-111ii−i−i002-200−2i2i−i3i3i3−i3−333−3-11-11i−ii−i0000000000000000
χ5422-2-222-2-2-1−2i−2i2i2i2-2−2i−2i2i2i2-2-1-1111-11iiii−i−i−i−i00000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333-1-111ii−i−i00-22002i−2ii3−i3−i3i33−3−331-11-1−ii−ii0000000000000000
χ5522-2-222-2-2-1−2i−2i2i2i2-2−2i−2i2i2i2-2-1-1111-11iiii−i−i−i−i00000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3-1-111ii−i−i002-200−2i2ii3−i3−i3i33−3−33-11-11i−ii−i0000000000000000
χ5622-2-222-2-2-1−2i−2i2i2i2-2−2i−2i2i2i2-2-1-1111-11iiii−i−i−i−i00000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3-1-111ii−i−i00-22002i−2i−i3i3i3−i3−333−31-11-1−ii−ii0000000000000000
χ5722-2-222-2-2-1−2i−2i2i2i-222i2i−2i−2i-22-1-1111-11iiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−311-1-1−i−iii2-200−2i2i00-11-11i−ii−i−i3i3i3−i3−333−30000000000000000
χ5822-2-222-2-2-1−2i−2i2i2i-222i2i−2i−2i-22-1-1111-11iiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−311-1-1−i−iii-22002i−2i001-11-1−ii−iii3−i3−i3i33−3−330000000000000000
χ5922-2-222-2-2-1−2i−2i2i2i-222i2i−2i−2i-22-1-1111-11iiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−33311-1-1−i−iii2-200−2i2i00-11-11i−ii−ii3−i3−i3i33−3−330000000000000000
χ6022-2-222-2-2-1−2i−2i2i2i-222i2i−2i−2i-22-1-1111-11iiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−33311-1-1−i−iii-22002i−2i001-11-1−ii−ii−i3i3i3−i3−333−30000000000000000
χ612-22-22-22-222i−2i2i−2i2-22i−2i2i−2i-22-2-222-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-22i−2i2i−2i000000000000000000000000000000002-22i−2i0000
χ622-22-22-22-222i−2i2i−2i2-22i−2i2i−2i-22-2-222-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-22i−2i2i−2i00000000000000000000000000000000-22−2i2i0000
χ632-22-22-22-222i−2i2i−2i-22−2i2i−2i2i2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-22−2i2i−2i2i0000000000000000000000000000000000002-22i−2i
χ642-22-22-22-222i−2i2i−2i-22−2i2i−2i2i2-2-2-222-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-22−2i2i−2i2i000000000000000000000000000000000000-22−2i2i
χ652-22-22-22-22−2i2i−2i2i2-2−2i2i−2i2i-22-2-222-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-2−2i2i−2i2i000000000000000000000000000000002-2−2i2i0000
χ662-22-22-22-22−2i2i−2i2i2-2−2i2i−2i2i-22-2-222-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-2−2i2i−2i2i00000000000000000000000000000000-222i−2i0000
χ672-22-22-22-22−2i2i−2i2i-222i−2i2i−2i2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-222i−2i2i−2i0000000000000000000000000000000000002-2−2i2i
χ682-22-22-22-22−2i2i−2i2i-222i−2i2i−2i2-2-2-222-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-222i−2i2i−2i000000000000000000000000000000000000-222i−2i
χ692-2-222-2-2222-2-22222-2-22-2-2-2-2-2-222222-2-2-2-2220000000000000000000000002-2-222-2-22000000000000000000000000002i−2i2i−2i0000000000
χ702-2-222-2-2222-2-22222-2-22-2-2-2-2-2-222222-2-2-2-2220000000000000000000000002-2-222-2-2200000000000000000000000000−2i2i−2i2i0000000000
χ712-2-222-2-2222-2-22-2-2-222-222-2-2-2-222222-2-2-2-222000000000000000000000000-222-2-222-20000000000000000000000002-200002-200000000
χ722-2-222-2-2222-2-22-2-2-222-222-2-2-2-222222-2-2-2-222000000000000000000000000-222-2-222-2000000000000000000000000-220000-2200000000
χ732-2-222-2-222-222-222-222-2-2-2-2-2-2-2222-2-22222-2-20000000000000000000000002-2-22-222-2000000000000000000000000002i−2i−2i2i0000000000
χ742-2-222-2-222-222-222-222-2-2-2-2-2-2-2222-2-22222-2-20000000000000000000000002-2-22-222-200000000000000000000000000−2i2i2i−2i0000000000
χ752-2-222-2-222-222-2-2-22-2-2222-2-2-2-2222-2-22222-2-2000000000000000000000000-222-22-2-220000000000000000000000002-20000-2200000000
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χ77444-4-4-4-4440000000000004-44-4-4-44000000000000004i−4i000000004i−4i4i−4i0000000000000000000000000000000000000000000000000000
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χ974-44-44-44-4-2−4i4i−4i4i4-4−4i4i−4i4i-4422-2-22-222i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-222i−2i2i−2i0000000000000000000000000000000000000000
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χ1024-4-444-4-44-2-444-4-4-44-4-44442222-2-2-222-2-2-2-2220000000000000000000000002-2-22-222-20000000000000000000000000000000000000000
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χ1084-4-4-4-4444-20000000000002-22-222-2−232323−2323−23−23230000-440000002-2-22000023−23−2323000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).