Finite Group Databasebeta

← Group #10691129

Character table — Group #10691129

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order122222344444466666664444444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-111-1-1-1-11-1-1111-1-11111-1-1ii−i−i-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-1-1-11-1-1111-1-11111-1-1ii−i−i-111-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-111-1-1-1-11-1-1111-1-11111-1-1−i−iii-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-111-1-1-1-11-1-1111-1-11111-1-1−i−iii-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-111-1-1-1-11-1-1111-1-111-1-111ii−i−i-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i-11i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-111-1-1-1-11-1-1111-1-111-1-111ii−i−i-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i-11i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-111-1-1-1-11-1-1111-1-111-1-111−i−iii-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii-11−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-111-1-1-1-11-1-1111-1-111-1-111−i−iii-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii-11−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-222222222-2-222220000-2-2-2-2-222222222222200000000-2-2000000-2-2-2-2-2-2000000000000000000000000
χ182222222222-2-222222222-2-2-2-2-2-20000-2-2-2-2-22222-2-2-2-2-2-2-2-20000000022000000-2-22222000000000000000000000000
χ192222222-2-2-222-222222222-200002222-22222-2-2-2-2000000002222222200-2-20000-2-20000-2-2-2-200000000000000000000
χ202222222-2-2-222-222222222-20000-2-2-2-2-22222-2-2-2-200000000-2-2-2-2-2-2-2-200220000-2-20000222200000000000000000000
χ212222222-2-2-2-2-2-22222222-22000000002-2-2-2-2-2-2-2-2000000000000000000002-22-2220000000022-2-222-2-2000000000000
χ222222222-2-2-2-2-2-22222222-22000000002-2-2-2-2-2-2-2-200000000000000000000-22-222200000000-2-222-2-222000000000000
χ23222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ25222222-1222222-1-1-1-1-1-1-122-2-2-2-222222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-11111-1-1-1-111111111000000000000
χ26222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-11111111111111111-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000
χ27222222-1222-2-22-1-1-1-1-1-1-1-2-222220000-21111-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i3-2-2000000111111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-1222-2-22-1-1-1-1-1-1-1-2-222220000-21111-1-1-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i3-2-2000000111111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-2-2-20000-21111-1-1-1-111111111−i3−i3i3i3−i3−i3i3i32200000011-1-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-2-2-20000-21111-1-1-1-111111111i3i3−i3−i3i3i3−i3−i32200000011-1-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-2-2-222-2-1-1-1-1-1-1-12-200002222-2-1-1-1-11111−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-100-2-2000011−i3i3−i3i31111−i3i3i3−i3−i3i3i3−i3000000000000
χ32222222-1-2-2-222-2-1-1-1-1-1-1-12-200002222-2-1-1-1-11111i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-100-2-2000011i3−i3i3−i31111i3−i3−i3i3i3−i3−i3i3000000000000
χ33222222-1-2-2-222-2-1-1-1-1-1-1-12-20000-2-2-2-2-2-1-1-1-11111−i3−i3i3i3−i3−i3i3i3111111110022000011−i3i3−i3i3-1-1-1-1i3−i3−i3i3i3−i3−i3i3000000000000
χ34222222-1-2-2-222-2-1-1-1-1-1-1-12-20000-2-2-2-2-2-1-1-1-11111i3i3−i3−i3i3i3−i3−i3111111110022000011i3−i3i3−i3-1-1-1-1−i3i3i3−i3−i3i3i3−i3000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000211111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300002-22-2-1-1i3−i3i3−i3i3−i3i3−i3-1-111-1-111000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000211111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000-22-22-1-1i3−i3i3−i3−i3i3−i3i311-1-111-1-1000000000000
χ37222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000211111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000-22-22-1-1−i3i3−i3i3i3−i3i3−i311-1-111-1-1000000000000
χ38222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2200000000211111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300002-22-2-1-1−i3i3−i3i3−i3i3−i3i3-1-111-1-111000000000000
χ392222-2-222-2-2222-2-2222-2-2-2-222-2-200002-2-22222-2-22222-2-2-2-200000000-22000000-22-2-222000000000000000000000000
χ402222-2-222-2-2222-2-2222-2-2-2-2-2-22200002-2-22222-2-2-2-2-2-22222000000002-2000000-2222-2-2000000000000000000000000
χ412222-2-22-22222-2-2-2222-2-2-2200000000-2-2-222-2-222000000000000000000002i−2i−2i2i2-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ422222-2-22-22222-2-2-2222-2-2-2200000000-2-2-222-2-22200000000000000000000−2i2i2i−2i2-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ432222-2-22-222-2-2-2-2-2222-2-22-200002i2i−2i−2i222-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i00−2i2i0000-220000−2i−2i2i2i00000000000000000000
χ442222-2-22-222-2-2-2-2-2222-2-22-20000−2i−2i2i2i222-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i002i−2i0000-2200002i2i−2i−2i00000000000000000000
χ452222-2-2-12-2-222211-1-1-111-2-222-2-20000211-1-1-1-111-1-1-1-1111133−3−3−3−333-220000001-111-1-13−3−333−33−3−33−33000000000000
χ462222-2-2-12-2-222211-1-1-111-2-222-2-20000211-1-1-1-111-1-1-1-11111−3−33333−3−3-220000001-111-1-1−333−3−33−333−33−3000000000000
χ472222-2-2-12-2-222211-1-1-111-2-2-2-2220000211-1-1-1-1111111-1-1-1-133−3−3−3−3332-20000001-1-1-1113−3−33−33−333−33−3000000000000
χ482222-2-2-12-2-222211-1-1-111-2-2-2-2220000211-1-1-1-1111111-1-1-1-1−3−33333−3−32-20000001-1-1-111−333−33−33−3−33−33000000000000
χ492222-2-2-12-2-2-2-2211-1-1-1112222-2-22i2i−2i−2i-2-1-111-1-111-1-1-1-11111−i−i−i−iiiii2-22i−2i2i2i−2i−2i-11-1-111−i−iii−i−i−i−iiiii000000000000
χ502222-2-2-12-2-2-2-2211-1-1-1112222-2-2−2i−2i2i2i-2-1-111-1-111-1-1-1-11111iiii−i−i−i−i2-2−2i2i−2i−2i2i2i-11-1-111ii−i−iiiii−i−i−i−i000000000000
χ512222-2-2-12-2-2-2-2211-1-1-11122-2-2222i2i−2i−2i-2-1-111-1-1111111-1-1-1-1−i−i−i−iiiii-222i−2i−2i−2i2i2i-1111-1-1−i−iiiiiii−i−i−i−i000000000000
χ522222-2-2-12-2-2-2-2211-1-1-11122-2-222−2i−2i2i2i-2-1-111-1-1111111-1-1-1-1iiii−i−i−i−i-22−2i2i2i2i−2i−2i-1111-1-1ii−i−i−i−i−i−iiiii000000000000
χ532222-2-2-1-22222-211-1-1-111-2200000000-211-1-111-1-1−i3−i3i3i3i3i3−i3−i333−3−3−3−33300002i−2i−2i2i-11i3−i3−i3i3−333−3−i−iiiii−i−i000000000000
χ542222-2-2-1-22222-211-1-1-111-2200000000-211-1-111-1-1−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000−2i2i2i−2i-11i3−i3−i3i33−3−33ii−i−i−i−iii000000000000
χ552222-2-2-1-22222-211-1-1-111-2200000000-211-1-111-1-1i3i3−i3−i3−i3−i3i3i333−3−3−3−3330000−2i2i2i−2i-11−i3i3i3−i3−333−3ii−i−i−i−iii000000000000
χ562222-2-2-1-22222-211-1-1-111-2200000000-211-1-111-1-1i3i3−i3−i3−i3−i3i3i3−3−33333−3−300002i−2i−2i2i-11−i3i3i3−i33−3−33−i−iiiii−i−i000000000000
χ572222-2-2-1-222-2-2-211-1-1-1112-200002i2i−2i−2i2-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i−i−i−iiiii00−2i2i00001-1−i3i3i3−i3ii−i−i3−3−33−333−3000000000000
χ582222-2-2-1-222-2-2-211-1-1-1112-200002i2i−2i−2i2-1-11111-1-1i3i3−i3−i3−i3−i3i3i3−i−i−i−iiiii00−2i2i00001-1i3−i3−i3i3ii−i−i−333−33−3−33000000000000
χ592222-2-2-1-222-2-2-211-1-1-1112-20000−2i−2i2i2i2-1-11111-1-1−i3−i3i3i3i3i3−i3−i3iiii−i−i−i−i002i−2i00001-1−i3i3i3−i3−i−iii−333−33−3−33000000000000
χ602222-2-2-1-222-2-2-211-1-1-1112-20000−2i−2i2i2i2-1-11111-1-1i3i3−i3−i3−i3−i3i3i3iiii−i−i−i−i002i−2i00001-1i3−i3−i3i3−i−iii3−3−33−333−3000000000000
χ612-2-222-22-22-200222-22-2-2-2002-22-20000000002-22-22-22-22-22-20000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ622-2-222-22-22-200222-22-2-2-2002-22-20000000002-22-22-22-22-22-20000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ632-2-222-22-22-200222-22-2-2-200-22-220000000002-22-2-22-22-22-220000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ642-2-222-22-22-200222-22-2-2-200-22-220000000002-22-2-22-22-22-220000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ652-2-22-222-2-22002-2-2-22-222002-2-220000000002-2-222-22-2-22-2200000000000000000000000000000000002−2−222−2−220000
χ662-2-22-222-2-22002-2-2-22-222002-2-220000000002-2-222-22-2-22-220000000000000000000000000000000000−222−2−222−20000
χ672-2-22-222-2-22002-2-2-22-22200-222-20000000002-2-22-22-222-22-200000000000000000000000000000000002−2−22−222−20000
χ682-2-22-222-2-22002-2-2-22-22200-222-20000000002-2-22-22-222-22-20000000000000000000000000000000000−222−22−2−220000
χ694-44-40040004i−4i000-4-44000000002+2i−2−2i2−2i−2+2i0004i−4i0000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000000000000000000000000
χ704-44-40040004i−4i000-4-4400000000−2−2i2+2i−2+2i2−2i0004i−4i000000000000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000000000000000000000000
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χ754-44-400-20004i−4i02i3−2i322-22i3−2i30000002+2i−2−2i2−2i−2+2i0−2323−2i2i000000000000−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ1400000000000000000000000000000000000000
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χ804-44-400-2000−4i4i02i3−2i322-22i3−2i3000000−2+2i2−2i−2−2i2+2i023−232i−2i0000000000002ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ1400000000000000000000000000000000000000
χ814-4-444-444-4400-444-44-4-4-4000000000000000-44-44000000000000000000000000000000000000000000000000000000
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χ854-4-444-4-2-44-4004-2-22-222200-44-44000000000-22-222-22-22-22-20000000000000000000000000000000000000000000000
χ864-4-44-44444-400-4-4-4-44-444000000000000000-444-4000000000000000000000000000000000000000000000000000000
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χ884-4-44-44-244-400-4222-22-2-20000000000000002-2-222i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ894-4-44-44-2-4-44004222-22-2-2004-4-44000000000-222-2-22-222-22-20000000000000000000000000000000000000000000000
χ904-4-44-44-2-4-44004222-22-2-200-444-4000000000-222-22-22-2-22-220000000000000000000000000000000000000000000000
χ9188-8-8008000000008-8-8000000000000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-800-4000000−4i34i3-4444i3−4i30000000000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-800-40000004i3−4i3-444−4i34i30000000000000000000000000000000000000000000000000000000000000000000000000

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