Finite Group Databasebeta

← Group #10694571

Character table — Group #10694571

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222344444444666888888881212121244668888121212121212121212122424242424242424242424242424242488888888888888882444661212121212124444
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−i1-11-111-1-111-1-1i−ii−i
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-11-11-1-111-1-111−ii−ii
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−iiiii1-11-111-1-111-1-1−ii−ii
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-11-11-1-111-1-111i−ii−i
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−iiiii1-1-1111-1-1-1-111i−i−ii
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-111-1-1-11111-1-1−iii−i
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−i1-1-1111-1-1-1-111−iii−i
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-111-1-1-11111-1-1i−i−ii
χ1722222222222-2-2-2-22222222-2-2-2-22222-2-222-2-222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222-2-2-2-222-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ202222222-2-2-2-222-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ212222222-2-2-2-2-2-22222200000000-2-2-2-2-22220000-2-222-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ222222222-2-2-2-2-2-22222200000000-2-2-2-2-22220000-2-222-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
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
χ27222222-12222-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-2-22211111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ28222222-12222-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-1-2-2-1-1-2-22211111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ29222222-12222-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-2-1-122-2-211111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ30222222-12222-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-2-2-1-122-2-211111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2222-2-222-2-2222000000002222-22-2-20000-2-22222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-2222-2-222-2-2222000000002222-22-2-20000-2-22222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-2222-2-2-2-2222220000000022222-2-2-2000022-2-2-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2222-2-2-2-2222220000000022222-2-2-2000022-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-22-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ362222-2-22-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-1-2-2222222-1-1-1222222221111-2-211-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-2-2-1-2-2222222-1-1-1222222221111-2-211-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-2-2-1-2-2222222-1-1-1-2-2-2-2-2-2-2-21111-2-21122221111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ402222-2-2-1-2-2222222-1-1-1-2-2-2-2-2-2-2-21111-2-21122221111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ412222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ422222-2-2-1-2-222-2-2-2-2-1-1-12222-2-2-2-21111221122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ432222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ442222-2-2-1-2-222-2-2-2-2-1-1-1-2-2-2-2222211112211-2-222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
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χ944-4-4400-20000−4i4i0022-2−2i22i22i2−2i2−222222−22−232323−230000000000−2i32i32i−2i0000i2−i2−i2i2−666−6−i6i6i6−i62−2−2200000000000000000000000000000000
χ954-4-4400-20000−4i4i0022-22i2−2i2−2i22i222−22−222223−23−232300000000002i3−2i32i−2i0000−i2i2i2−i2−666−6−i6i6i6−i6−222−200000000000000000000000000000000
χ964-4-4400-20000−4i4i0022-22i2−2i2−2i22i222−22−2222−232323−230000000000−2i32i32i−2i0000−i2i2i2−i26−6−66i6−i6−i6i6−222−200000000000000000000000000000000

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