Finite Group Databasebeta

← Group #10698564

Character table — Group #10698564

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222222344444444666666644888888881212121212121212121212122424242424242424242424242424242422446666121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ9222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000220000-2-200000000
χ10222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000-2-200002200000000
χ11222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-200000000000000000000000000000022-2-20000000000
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χ1722222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ1822222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-200-1-111−i3−i3i3i30000000000000000
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χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i30000000000000000
χ23222-2-22-2-220002-2-20222-22-2-2-200−i2−i2−i2−i2i2i2i2i2000022-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000000000002i−2i00000022−2−2
χ24222-2-22-2-220002-2-20222-22-2-2-200−i2−i2−i2−i2i2i2i2i2000022-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000−2i2i000000−2−222
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χ2722-222-2-2-222-2-2000202-22-22-2-200−i2−i2i2i2−i2−i2i2i222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000002i−2i22−2−20000
χ2822-222-2-2-222-2-2000202-22-22-2-200−i2−i2i2i2−i2−i2i2i222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000−2i2i−2−2220000
χ2922-222-2-2-222-2-2000202-22-22-2-200i2i2−i2−i2i2i2−i2−i222-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000002i−2i−2−2220000
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χ312-222-2-2-22222-2000-20-22-2-22-22002−22−22−22−22-22-2000000002−22−22−22−22−22−22−22−20000000000002i−2i000000−i2i2−i2i20000
χ322-222-2-2-22222-2000-20-22-2-22-22002−22−22−22−22-22-2000000002−22−22−22−22−22−22−22−2000000000000−2i2i000000i2−i2i2−i20000
χ332-222-2-2-22222-2000-20-22-2-22-2200−22−22−22−222-22-200000000−22−22−22−22−22−22−22−220000000000002i−2i000000i2−i2i2−i20000
χ342-222-2-2-22222-2000-20-22-2-22-2200−22−22−22−222-22-200000000−22−22−22−22−22−22−22−22000000000000−2i2i000000−i2i2−i2i20000
χ352-2-22-222-222-2222-2-2-2-2-2-2222-2-22000000002-2-222-22-2-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ362-2-22-222-222-2222-2-2-2-2-2-2222-2-22000000002-2-222-22-2-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ372-2-22-222-222-22-2-22-22-2-2-2222-22-22i−2i−2i2i2i−2i−2i2i2-2-22-22-2222-2-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ382-2-22-222-222-22-2-22-22-2-2-2222-22-2−2i2i2i−2i−2i2i2i−2i2-2-22-22-2222-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ392-2-22-222-22-22-222-22-2-2-2-2222-22-200000000-222-22-22-222-2-20000000000000000002i−2i00002i−2i2i−2i0000000000000000
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χ412-2-22-222-22-22-2-2-2222-2-2-2222-2-2200000000-222-2-22-22-2-22200000000000000000000000000000000000000002-22-2
χ422-2-22-222-22-22-2-2-2222-2-2-2222-2-2200000000-222-2-22-22-2-2220000000000000000000000000000000000000000-22-22
χ432-2-22-222-2-12-22-2-22-22111-1-1-112-22i−2i−2i2i2i−2i−2i2i-111-11-11-1-1-111−iii−i−iii−i−iii−i−iii−i0000−i3i3−i3i33−3−330000000000000000
χ442-2-22-222-2-12-22-2-22-22111-1-1-112-22i−2i−2i2i2i−2i−2i2i-111-11-11-1-1-111−iii−i−iii−i−iii−i−iii−i0000i3−i3i3−i3−333−30000000000000000
χ452-2-22-222-2-12-22-2-22-22111-1-1-112-2−2i2i2i−2i−2i2i2i−2i-111-11-11-1-1-111i−i−iii−i−iii−i−iii−i−ii0000−i3i3−i3i3−333−30000000000000000
χ462-2-22-222-2-12-22-2-22-22111-1-1-112-2−2i2i2i−2i−2i2i2i−2i-111-11-11-1-1-111i−i−iii−i−iii−i−iii−i−ii0000i3−i3i3−i33−3−330000000000000000
χ472-2-22-222-2-1-22-222-22-2111-1-1-112-2000000001-1-11-11-11-1-1113−3−333−3−33−333−3−333−3002i−2i−i3i3i3−i3−ii−ii0000000000000000
χ482-2-22-222-2-1-22-222-22-2111-1-1-112-2000000001-1-11-11-11-1-1113−3−333−3−33−333−3−333−300−2i2ii3−i3−i3i3i−ii−i0000000000000000
χ492-2-22-222-2-1-22-222-22-2111-1-1-112-2000000001-1-11-11-11-1-111−333−3−333−33−3−333−3−33002i−2ii3−i3−i3i3−ii−ii0000000000000000
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χ512-2-2-222-222000-22-202-2-222-2-22002−2−22−222−20000-222-200002−2−22−222−22−2−22−222−2000000000000002-2000000002−2−22
χ522-2-2-222-222000-22-202-2-222-2-22002−2−22−222−20000-222-200002−2−22−222−22−2−22−222−200000000000000-2200000000−222−2
χ532-2-2-222-222000-22-202-2-222-2-2200−222−22−2−220000-222-20000−222−22−2−22−222−22−2−22000000000000002-200000000−222−2
χ542-2-2-222-222000-22-202-2-222-2-2200−222−22−2−220000-222-20000−222−22−2−22−222−22−2−2200000000000000-22000000002−2−22
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4000000002222-2-2-2-2222200000000000000000000000000000000000000000000
χ57444-4-44-4-44000-4440-444-44-4-4-400000000000000-4-444000000000000000000000000000000000000000000000000
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χ59444-4-44-4-4-20004-4-404-2-22-2222002i22i22i22i2−2i2−2i2−2i2−2i20000-2-2220000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000
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χ6444-444-4-4-4-24-4-400040-22-22-222002i22i2−2i2−2i22i22i2−2i2−2i2-2-22200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ6544-444-4-4-4-2-444000-40-22-22-222000000000022-2-20000000066−6−666−6−6−6−666−6−6660000000000000000000000000000
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χ794-44-44-44-4400000000-444-4-44-400−2i2i−2i2i2i−2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ804-44-44-44-4-2000000002-2-222-22002i−2i2i−2i−2i2i−2i2i00000000−2i32i32i3−2i32ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ140000000000000000000000000000
χ814-44-44-44-4-2000000002-2-222-22002i−2i2i−2i−2i2i−2i2i000000002i3−2i3−2i32i32ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ220000000000000000000000000000
χ824-44-44-44-4-2000000002-2-222-2200−2i2i−2i2i2i−2i2i−2i00000000−2i32i32i3−2i3−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ140000000000000000000000000000
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χ854-4-44-444-4-2-44-4-4-4444222-2-2-22-44000000002-2-222-22-222-2-200000000000000000000000000000000000000000000
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χ874-4-4-444-44-20004-440-422-2-222-200000000000000-222-20000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-4-444-44-20004-440-422-2-222-200000000000000-222-20000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-4-444-44-2000-44-40422-2-222-20022−22−2222−222222−2200002-2-220000−222−22−2−22−222−22−2−220000000000000000000000000000
χ904-4-4-444-44-2000-44-40422-2-222-200−222222−2222−22−222200002-2-2200002−2−22−222−22−2−22−222−20000000000000000000000000000

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