Finite Group Databasebeta

← Group #10694032

Character table — Group #10694032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222234444444466666661212121212121212444444446666121212121212121212121212121212121212121288888888242424242424242424242424242424244444444488888888
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ121111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ131111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ18222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ21222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ22222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ2522222222-2-2-2-222222-2-2-2-222222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2622222222-2-2-2-222222-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2722222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3222222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ3722-2-22-22-222-2-222i−2i2i−2i2i2i−2i−2i22-2-22-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i0000000000000000000000000000000000000000002-2002i−2i00000000
χ3822-2-22-22-222-2-222i−2i2i−2i2i2i−2i−2i22-2-22-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i000000000000000000000000000000000000000000-2200−2i2i00000000
χ3922-2-22-22-222-2-22−2i2i−2i2i−2i−2i2i2i22-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i0000000000000000000000000000000000000000002-200−2i2i00000000
χ4022-2-22-22-222-2-22−2i2i−2i2i−2i−2i2i2i22-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i000000000000000000000000000000000000000000-22002i−2i00000000
χ4122-2-22-22-2-2-22222i−2i2i−2i−2i−2i2i2i22-2-22-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i−2i2i2i00000000000000000000000000000000000000002-2002i−2i0000000000
χ4222-2-22-22-2-2-22222i−2i2i−2i−2i−2i2i2i22-2-22-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i−2i2i2i0000000000000000000000000000000000000000-2200−2i2i0000000000
χ4322-2-22-22-2-2-2222−2i2i−2i2i2i2i−2i−2i22-2-22-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i2i−2i−2i00000000000000000000000000000000000000002-200−2i2i0000000000
χ4422-2-22-22-2-2-2222−2i2i−2i2i2i2i−2i−2i22-2-22-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i2i−2i−2i0000000000000000000000000000000000000000-22002i−2i0000000000
χ452-22-2-222-22-22-222i−2i−2i2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i−2i−2i2i2i000000002-22-22i−2i2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ462-22-2-222-22-22-222i−2i−2i2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i−2i−2i2i2i000000002-22-22i−2i2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ472-22-2-222-22-22-22−2i2i2i−2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2i2i−2i−2i000000002-22-2−2i2i−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ482-22-2-222-22-22-22−2i2i2i−2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2i2i−2i−2i000000002-22-2−2i2i−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ492-22-2-222-22-22-2-12i−2i−2i2i2i−2i2i−2i-11-111-11−i−iiiii−i−i00000000-11-11−ii−ii33−3−333−3−3−i3−i3i3i3−i3−i3i3i300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ130000000000000000
χ502-22-2-222-22-22-2-12i−2i−2i2i2i−2i2i−2i-11-111-11−i−iiiii−i−i00000000-11-11−ii−ii33−3−333−3−3−i3−i3i3i3−i3−i3i3i30000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ130000000000000000
χ512-22-2-222-22-22-2-12i−2i−2i2i2i−2i2i−2i-11-111-11−i−iiiii−i−i00000000-11-11−ii−ii−3−333−3−333i3i3−i3−i3i3i3−i3−i300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ130000000000000000
χ522-22-2-222-22-22-2-12i−2i−2i2i2i−2i2i−2i-11-111-11−i−iiiii−i−i00000000-11-11−ii−ii−3−333−3−333i3i3−i3−i3i3i3−i3−i30000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ130000000000000000
χ532-22-2-222-22-22-2-1−2i2i2i−2i−2i2i−2i2i-11-111-11ii−i−i−i−iii00000000-11-11i−ii−i33−3−333−3−3i3i3−i3−i3i3i3−i3−i30000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ230000000000000000
χ542-22-2-222-22-22-2-1−2i2i2i−2i−2i2i−2i2i-11-111-11ii−i−i−i−iii00000000-11-11i−ii−i33−3−333−3−3i3i3−i3−i3i3i3−i3−i300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ230000000000000000
χ552-22-2-222-22-22-2-1−2i2i2i−2i−2i2i−2i2i-11-111-11ii−i−i−i−iii00000000-11-11i−ii−i−3−333−3−333−i3−i3i3i3−i3−i3i3i30000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ230000000000000000
χ562-22-2-222-22-22-2-1−2i2i2i−2i−2i2i−2i2i-11-111-11ii−i−i−i−iii00000000-11-11i−ii−i−3−333−3−333−i3−i3i3i3−i3−i3i3i300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ230000000000000000
χ572-22-2-222-2-22-2222i−2i−2i2i−2i2i−2i2i2-22-2-22-22i2i−2i−2i−2i−2i2i2i00000000-22-22−2i2i−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ582-22-2-222-2-22-2222i−2i−2i2i−2i2i−2i2i2-22-2-22-22i2i−2i−2i−2i−2i2i2i00000000-22-22−2i2i−2i2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ592-22-2-222-2-22-222−2i2i2i−2i2i−2i2i−2i2-22-2-22-2−2i−2i2i2i2i2i−2i−2i00000000-22-222i−2i2i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.