Finite Group Databasebeta

← Group #10694598

Character table — Group #10694598

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222234444444466688888888121212124466888812121212121212121212242424242424242424242424242424244444444488888888888824242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-11-11
χ121111-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii1-11-1
χ131111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ141111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ151111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111-1-11-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ17222222222-2-2-2-2-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-2-2-2-2-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222-2-222-2-22222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222-2-222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ212222222-2-2-2-222-2-2222000000002222-22220000-2-222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ222222222-2-2-2-222-2-2222000000002222-22220000-2-222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ23222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ24222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ25222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ26222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ27222222-1-2-222-2-222-1-1-1222222221111-2-2-1-1-2-2-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000000000003−33−33−33−30000
χ28222222-1-2-222-2-222-1-1-1222222221111-2-2-1-1-2-2-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−33−33−33−330000
χ29222222-1-2-222-2-222-1-1-1-2-2-2-2-2-2-2-21111-2-2-1-12222111111-1-1-1-11111-1-1-1-11111-1-1-1-1000000000000000000003−33−3−33−330000
χ30222222-1-2-222-2-222-1-1-1-2-2-2-2-2-2-2-21111-2-2-1-12222111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−33−333−33−30000
χ312222-2-22222222-2-22222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ322222-2-22222222-2-2222-2-2-2-222222222-2-2-2-222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
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χ342222-2-2222-2-2-2-22222200000000-2-2-2-2-22-2-20000-2-2222222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352222-2-22-2-2-2-222222220000000022222-2-2-2000022-2-2-2-222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ362222-2-22-2-2-2-222222220000000022222-2-2-2000022-2-2-2-222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ372222-2-2-1222222-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-2-2-1222222-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-2-2-1222222-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ402222-2-2-1222222-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ412222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ422222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ432222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ442222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ452-22-20022i−2i2-22i−2i002-2-2000022-2-22i2i−2i−2i00002i−2i0000002i−2i002-200002i2i−2i−2i22-2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-22-20022i−2i2-22i−2i002-2-2000022-2-22i2i−2i−2i00002i−2i0000002i−2i002-200002i2i−2i−2i22-2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-22-20022i−2i2-22i−2i002-2-20000-2-2222i2i−2i−2i0000−2i2i0000002i−2i002-20000−2i−2i2i2i-2-22200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-22-20022i−2i2-22i−2i002-2-20000-2-2222i2i−2i−2i0000−2i2i0000002i−2i002-20000−2i−2i2i2i-2-2220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-20022i−2i-22−2i2i002-2-22i2i−2i−2i0000−2i−2i2i2i0000002-200002i−2i00-222i2i−2i−2i0000000022-2-21−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ502-22-20022i−2i-22−2i2i002-2-22i2i−2i−2i0000−2i−2i2i2i0000002-200002i−2i00-222i2i−2i−2i0000000022-2-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ512-22-20022i−2i-22−2i2i002-2-2−2i−2i2i2i0000−2i−2i2i2i000000-2200002i−2i00-22−2i−2i2i2i00000000-2-2221−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ522-22-20022i−2i-22−2i2i002-2-2−2i−2i2i2i0000−2i−2i2i2i000000-2200002i−2i00-22−2i−2i2i2i00000000-2-222−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ532-22-2002−2i2i2-2−2i2i002-2-2000022-2-2−2i−2i2i2i0000−2i2i000000−2i2i002-20000−2i−2i2i2i22-2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ542-22-2002−2i2i2-2−2i2i002-2-2000022-2-2−2i−2i2i2i0000−2i2i000000−2i2i002-20000−2i−2i2i2i22-2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ552-22-2002−2i2i2-2−2i2i002-2-20000-2-222−2i−2i2i2i00002i−2i000000−2i2i002-200002i2i−2i−2i-2-22200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ562-22-2002−2i2i2-2−2i2i002-2-20000-2-222−2i−2i2i2i00002i−2i000000−2i2i002-200002i2i−2i−2i-2-2220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
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χ582-22-2002−2i2i-222i−2i002-2-22i2i−2i−2i00002i2i−2i−2i000000-220000−2i2i00-222i2i−2i−2i00000000-2-222−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
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χ914-4-4400-20000004i−4i22-22i2−2i2−2i22i2−222222−22−2i32i32i3−2i30000000023−230000−2i2i00−i2i2i2−i2i6−i6−i6i62−2−226−6−6600000000000000000000000000000000
χ924-4-4400-20000004i−4i22-22i2−2i2−2i22i2−222222−222i3−2i3−2i32i300000000−23230000−2i2i00−i2i2i2−i2−i6i6i6−i62−2−22−666−600000000000000000000000000000000
χ934-4-4400-2000000−4i4i22-2−2i22i22i2−2i2−222222−22−2i32i32i3−2i300000000−232300002i−2i00i2−i2−i2i2i6−i6−i6i62−2−22−666−600000000000000000000000000000000
χ944-4-4400-2000000−4i4i22-2−2i22i22i2−2i2−222222−222i3−2i3−2i32i30000000023−2300002i−2i00i2−i2−i2i2−i6i6i6−i62−2−226−6−6600000000000000000000000000000000
χ954-4-4400-2000000−4i4i22-22i2−2i2−2i22i222−22−2222−2i32i32i3−2i300000000−232300002i−2i00−i2i2i2−i2−i6i6i6−i6−222−26−6−6600000000000000000000000000000000
χ964-4-4400-2000000−4i4i22-22i2−2i2−2i22i222−22−22222i3−2i3−2i32i30000000023−2300002i−2i00−i2i2i2−i2i6−i6−i6i6−222−2−666−600000000000000000000000000000000

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