Finite Group Databasebeta

← Group #10694896

Character table — Group #10694896

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222344444466666668888888824666688881212121212121212242424242424242424242424242424244444444488888888444412121212121212128888
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
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-11111-1-1
χ9111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−ii−i
χ10111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111−ii−ii
χ11111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ii
χ12111111-1-1111-1-1-1-111111111111-1-1-1-1-11-1-1-1-111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111i−ii−i
χ13111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ14111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ15111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ16111111-1-1111-1-1-1-11111111-1-1-1-11111-11-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ17222222222-2-2-2-2-2-22222222000000002-222220000-2-2-2-2-2-2-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222-2-2-2-2-2-22222222000000002-222220000-2-2-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ1922222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-1222222-1-1-1-1-1-1-12222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000002-22-2-1-111-1-1110000
χ2222222222-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000-22-2211-1-111-1-10000
χ23222222-2-22-2-22222222222200000000-2-2-2-2-2-20000-2-2-22222-200000000000000000000000022-2-2-2-2220000000000000000
χ24222222-2-22-2-22222222222200000000-2-2-2-2-2-20000-2-2-22222-2000000000000000000000000-2-22222-2-20000000000000000
χ25222222-2-2-122-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-22111122-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ26222222-2-2-122-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-22111122-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ27222222-2-2-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-221111-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ28222222-2-2-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-221111-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ292222-2-22222222-2-22-2-2-2-22222222222-2-222-2-2-2-2-2-22-2-222-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-22222222-2-22-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-222222-2-222-2-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
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χ322222-2-2222-2-2-2-2222-2-2-2-22200000000-2222-2-20000-222-2-222-20000000000000000-2-222-2-222000000000000000000000000
χ332222-2-222-12222-2-2-11111-1-122222222-2-2-1-111-2-2-2-2-111-1-111-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ342222-2-222-12222-2-2-11111-1-122222222-2-2-1-111-2-2-2-2-111-1-111-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ352222-2-222-12222-2-2-11111-1-1-2-2-2-2-2-2-2-2-2-2-1-1112222-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ362222-2-222-12222-2-2-11111-1-1-2-2-2-2-2-2-2-2-2-2-1-1112222-111-1-111-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ372222-2-2-2-2222-2-2222-2-2-2-2222222-2-2-2-22-2-2-222-2-2222-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ382222-2-2-2-2222-2-2222-2-2-2-222-2-2-2-222222-2-2-22222-2-22-2-2-2-2222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ392222-2-2-2-22-2-222-2-22-2-2-2-2220000000022-2-2220000-22222-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-22-2-222-2-22-2-2-2-2220000000022-2-2220000-22222-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-122-2-222-11111-1-12222-2-2-2-22-211-1-1-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ422222-2-2-2-2-122-2-222-11111-1-12222-2-2-2-22-211-1-1-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ432222-2-2-2-2-122-2-222-11111-1-1-2-2-2-222222-211-1-122-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442222-2-2-2-2-122-2-222-11111-1-1-2-2-2-222222-211-1-122-2-2-11111-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
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χ462-22-22-2002002i−2i2i−2i-222-2-22-222−2−2−i2−i2i2i20000002−2−i2i20002i−2i2i−2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ472-22-22-2002002i−2i2i−2i-222-2-22-2−2−222i2i2−i2−i2000000−22i2−i20002i−2i2i−2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ482-22-22-2002002i−2i2i−2i-222-2-22-2−2−222i2i2−i2−i2000000−22i2−i20002i−2i2i−2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ492-22-22-200200−2i2i−2i2i-222-2-22-222−2−2i2i2−i2−i20000002−2i2−i2000−2i2i−2i2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ502-22-22-200200−2i2i−2i2i-222-2-22-222−2−2i2i2−i2−i20000002−2i2−i2000−2i2i−2i2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ512-22-22-200200−2i2i−2i2i-222-2-22-2−2−222−i2−i2i2i2000000−22−i2i2000−2i2i−2i2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ522-22-22-200200−2i2i−2i2i-222-2-22-2−2−222−i2−i2i2i2000000−22−i2i2000−2i2i−2i2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ532-22-2-22002002i−2i−2i2i-2-2-2222-222−2−2−i2−i2i2i2000000−22i2−i20002i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ542-22-2-22002002i−2i−2i2i-2-2-2222-222−2−2−i2−i2i2i2000000−22i2−i20002i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ552-22-2-22002002i−2i−2i2i-2-2-2222-2−2−222i2i2−i2−i20000002−2−i2i20002i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ562-22-2-22002002i−2i−2i2i-2-2-2222-2−2−222i2i2−i2−i20000002−2−i2i20002i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ572-22-2-2200200−2i2i2i−2i-2-2-2222-222−2−2i2i2−i2−i2000000−22−i2i2000−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ582-22-2-2200200−2i2i2i−2i-2-2-2222-222−2−2i2i2−i2−i2000000−22−i2i2000−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ592-22-2-2200200−2i2i2i−2i-2-2-2222-2−2−222−i2−i2i2i20000002−2i2−i2000−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ602-22-2-2200200−2i2i2i−2i-2-2-2222-2−2−222−i2−i2i2i20000002−2i2−i2000−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ6144444444-2-4-4-4-4-4-4-2-2-2-2-2-2-2000000004-4-2-2-2-2000022222222000000000000000000000000000000000000000000000000
χ62444444-4-4-2-4-44444-2-2-2-2-2-2-200000000-4-422220000222-2-2-2-22000000000000000000000000000000000000000000000000
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χ7044-4-4004-4-2000000-22i3−2i32i3−2i322−2222−2222−2222−222200-222i3−2i30000000000002−22−2i6−i6i6−i62−22−2i6−i6i6−i600000000000000000000000000000000
χ7144-4-400-44400000040000-4-422−2222−22−2222−222200-440000000000000022−2222−220000−2222−2222000000000000000000000000000000000000
χ7244-4-400-44400000040000-4-4−2222−222222−2222−2200-4400000000000000−2222−2222000022−2222−22000000000000000000000000000000000000
χ7344-4-400-44-2000000-2−2i32i3−2i32i32222−2222−22−2222−2222002-22i3−2i3000000000000−22−22i6−i6i6−i62−22−2−i6i6−i6i600000000000000000000000000000000
χ7444-4-400-44-2000000-2−2i32i3−2i32i322−2222−222222−2222−22002-22i3−2i30000000000002−22−2−i6i6−i6i6−22−22i6−i6i6−i600000000000000000000000000000000
χ7544-4-400-44-2000000-22i3−2i32i3−2i32222−2222−22−2222−2222002-2−2i32i3000000000000−22−22−i6i6−i6i62−22−2i6−i6i6−i600000000000000000000000000000000
χ7644-4-400-44-2000000-22i3−2i32i3−2i322−2222−222222−2222−22002-2−2i32i30000000000002−22−2i6−i6i6−i6−22−22−i6i6−i6i600000000000000000000000000000000
χ774-44-44-400-2004i−4i4i−4i2-2-222-222222−22−22−2i2−2i22i22i200000022−22−2i22i2000−2i2i−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ784-44-44-400-2004i−4i4i−4i2-2-222-22−22−2222222i22i2−2i2−2i2000000−22222i2−2i2000−2i2i−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ794-44-44-400-200−4i4i−4i4i2-2-222-222222−22−222i22i2−2i2−2i200000022−222i2−2i20002i−2i2i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ804-44-44-400-200−4i4i−4i4i2-2-222-22−22−222222−2i2−2i22i22i2000000−2222−2i22i20002i−2i2i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ814-44-4-4400-2004i−4i−4i4i222-2-2-222222−22−22−2i2−2i22i22i2000000−22222i2−2i2000−2i2i2i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ824-44-4-4400-2004i−4i−4i4i222-2-2-22−22−2222222i22i2−2i2−2i200000022−22−2i22i2000−2i2i2i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ834-44-4-4400-200−4i4i4i−4i222-2-2-222222−22−222i22i2−2i2−2i2000000−2222−2i22i20002i−2i−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ844-44-4-4400-200−4i4i4i−4i222-2-2-22−22−222222−2i2−2i22i22i200000022−222i2−2i20002i−2i−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ854-4-44000044-40000-40000-4400004i−4i−4i4i00000000004000000-4000000004i−4i−4i4i000000000000000000000000000000000000
χ864-4-44000044-40000-40000-440000−4i4i4i−4i00000000004000000-400000000−4i4i4i−4i000000000000000000000000000000000000
χ874-4-4400004-440000-40000-444-4-4400000000000000-400000044-4-4400000000000000000000000000000000000000000000
χ884-4-4400004-440000-40000-44-444-400000000000000-40000004-444-400000000000000000000000000000000000000000000
χ894-4-440000-24-400002−2i32i32i3−2i32-200004i−4i−4i4i0000000000-2−2i32i30000200000000−2i2i2i−2i−232323−2300000000000000000000000000000000
χ904-4-440000-24-400002−2i32i32i3−2i32-20000−4i4i4i−4i0000000000-2−2i32i300002000000002i−2i−2i2i23−23−232300000000000000000000000000000000
χ914-4-440000-24-4000022i3−2i3−2i32i32-200004i−4i−4i4i0000000000-22i3−2i30000200000000−2i2i2i−2i23−23−232300000000000000000000000000000000
χ924-4-440000-24-4000022i3−2i3−2i32i32-20000−4i4i4i−4i0000000000-22i3−2i300002000000002i−2i−2i2i−232323−2300000000000000000000000000000000
χ934-4-440000-2-4400002−2i32i32i3−2i32-24-4-440000000000000022i3−2i30000-2-222-22i3−2i3−2i32i30000000000000000000000000000000000000000
χ944-4-440000-2-4400002−2i32i32i3−2i32-2-444-40000000000000022i3−2i30000-22-2-22−2i32i32i3−2i30000000000000000000000000000000000000000
χ954-4-440000-2-44000022i3−2i3−2i32i32-24-4-44000000000000002−2i32i30000-2-222-2−2i32i32i3−2i30000000000000000000000000000000000000000
χ964-4-440000-2-44000022i3−2i3−2i32i32-2-444-4000000000000002−2i32i30000-22-2-222i3−2i3−2i32i30000000000000000000000000000000000000000

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