Finite Group Databasebeta

← Group #10690736

Character table — Group #10690736

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212124444888888881212121212121212242424242424242424242424242424242444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1111111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1111-1-1-1ii−i−iii−i−i
χ1011111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-1-1111−i−iii−i−iii
χ1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1111-1-1-1−i−iii−i−iii
χ1211111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-1-1111ii−i−iii−i−i
χ1311111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111ii−i−i−i−iii
χ1411111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1−i−iiiii−i−i
χ1511111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111−i−iiiii−i−i
χ1611111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1ii−i−i−i−iii
χ172222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ222222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ25222222-2-2-2-222222-2-2-2-2222222222-2-2-2-222-2-2-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ26222222-2-2-2-222222-2-2-2-2222222222-2-2-2-222-2-2-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ27222222-2-2-2-22-2-2-2-22222222-2-2-2-222-2-2-2-2-2-22222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ28222222-2-2-2-22-2-2-2-22222222-2-2-2-222-2-2-2-2-2-2222200000000-222-20000000000000000-2-22222-2-20000000000000000
χ29222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111000000002i−2i2i−2i33−3−333−3−3−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000000000000000
χ30222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111000000002i−2i2i−2i−3−333−3−333i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii0000000000000000
χ31222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111100000000−2i2i−2i2i33−3−333−3−3i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000000000000000
χ32222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111100000000−2i2i−2i2i−3−333−3−333−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i0000000000000000
χ33222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1000000002-2-2233−3−3−3−333−3−33333−3−3-1-11111-1-10000000000000000
χ34222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1000000002-2-22−3−33333−3−333−3−3−3−333-1-11111-1-10000000000000000
χ35222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-100000000-222-233−3−3−3−33333−3−3−3−33311-1-1-1-1110000000000000000
χ36222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-100000000-222-2−3−33333−3−3−3−33333−3−311-1-1-1-1110000000000000000
χ372222-2-222-2-2222-2-222-2-2222-2-2-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ382222-2-222-2-2222-2-222-2-2222-2-2-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ392222-2-222-2-22-2-222-2-2222222222-2-222-2-2-2-2-2-2220000000000000000000000000000000000000000000000002-2-22
χ402222-2-222-2-22-2-222-2-2222222222-2-222-2-2-2-2-2-222000000000000000000000000000000000000000000000000-222-2
χ412222-2-2-2-222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000000000002-2-20020000000000
χ422222-2-2-2-222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-222000000000000000000000000000000000000-22200-20000000000
χ432222-2-2-2-2222-2-22222-2-22222222-2-2-2-222-2-222-2-200000000000000000000000000000000000022-200-20000000000
χ442222-2-2-2-2222-2-22222-2-22222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000-2-220020000000000
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χ472-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i2-2-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000002-20−2i2i00000000
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χ492-22-22-2-22-2222i−2i2i−2i−2i2i−2i2i2-2-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ502-22-22-2-22-2222i−2i2i−2i−2i2i−2i2i2-2-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ512-22-22-2-22-222−2i2i−2i2i2i−2i2i−2i2-2-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ522-22-22-2-22-222−2i2i−2i2i2i−2i2i−2i2-2-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
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χ542-22-2-222-2-2222i−2i−2i2i2i−2i−2i2i2-2-2−2i−2i2i2i-222-2-222i−2i2i−2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ552-22-2-222-2-222−2i2i2i−2i−2i2i2i−2i2-2-22i2i−2i−2i-222-2-22−2i2i−2i2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ562-22-2-222-2-222−2i2i2i−2i−2i2i2i−2i2-2-22i2i−2i−2i-222-2-22−2i2i−2i2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ572-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i-111ii−i−i1-1-111-1−ii−iii−i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300003−33−3−i3i3−i3i3ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ582-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i-111ii−i−i1-1-111-1−ii−iii−i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−33−33i3−i3i3−i3ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ592-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i-111ii−i−i1-1-111-1−ii−iii−i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300003−33−3−i3i3−i3i3−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ602-22-2-222-2-22-12i−2i−2i2i2i−2i−2i2i-111ii−i−i1-1-111-1−ii−iii−i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−33−33i3−i3i3−i3−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ612-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i-111−i−iii1-1-111-1i−ii−i−ii00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300003−33−3i3−i3i3−i3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000000
χ622-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i-111−i−iii1-1-111-1i−ii−i−ii00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−33−33−i3i3−i3i3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ632-22-2-222-2-22-1−2i2i2i−2i−2i2i2i−2i-111−i−iii1-1-111-1i−ii−i−ii0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300003−33−3i3−i3i3−i3ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000000
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χ672-22-2-22-222-22−2i2i2i−2i2i−2i−2i2i2-2-22i2i−2i−2i-22-222-2−2i2i2i−2i−2i2i2-2−2i2i000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ682-22-2-22-222-22−2i2i2i−2i2i−2i−2i2i2-2-22i2i−2i−2i-22-222-2−2i2i2i−2i−2i2i-222i−2i00000000-222-2−2i2i2i−2i00000000000000000000000000000000
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χ712-22-2-22-222-2-12i−2i−2i2i−2i2i2i−2i-111ii−i−i1-11-1-11−iii−i−ii-22−2i2i000000001-1-11−iii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000000
χ722-22-2-22-222-2-12i−2i−2i2i−2i2i2i−2i-111ii−i−i1-11-1-11−iii−i−ii-22−2i2i000000001-1-11−iii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000000
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χ742-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i-111−i−iii1-11-1-11i−i−iii−i2-2−2i2i00000000-111-1−iii−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ752-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i-111−i−iii1-11-1-11i−i−iii−i-222i−2i000000001-1-11i−i−ii−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ762-22-2-22-222-2-1−2i2i2i−2i2i−2i−2i2i-111−i−iii1-11-1-11i−i−iii−i-222i−2i000000001-1-11i−i−iiζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ774444-4-444-4-4-244-4-444-4-4-2-2-2222222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ784444-4-444-4-4-2-4-444-4-444-2-2-2-2-2-2-222-2-2222222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-244-4-4-4-444-2-2-222222222-2-2-2-222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-4-44444-4-4-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ814-44-44-44-44-4-24i−4i4i−4i4i−4i4i−4i-222−2i−2i2i2i-22-22-22−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ824-44-44-44-44-4-2−4i4i−4i4i−4i4i−4i4i-2222i2i−2i−2i-22-22-222i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ834-44-44-4-44-44-24i−4i4i−4i−4i4i−4i4i-222−2i−2i2i2i-222-22-2−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ844-44-44-4-44-44-2−4i4i−4i4i4i−4i4i−4i-2222i2i−2i−2i-222-22-22i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8588-8-8000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-4000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-40000000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-40000000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000

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